BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicholas J. Higham (University of Manchester\, UK) DTSTART:20200429T140000Z DTEND:20200429T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/2 DESCRIPTION:Title: Ar e Numerical Linear Algebra Algorithms Accurate at Extreme Scale and at Low Precisions?\nby Nicholas J. Higham (University of Manchester\, UK) as part of E-NLA - Online seminar series on numerical linear algebra\n\n\nAb stract\nThe advent of exascale computing will bring the capability to solv e dense linear systems of order $10^8$. At the same time\, computer hardwa re is increasingly supporting low precision floating-point arithmetics\, s uch as the IEEE half precision and bfloat16 arithmetics. The standard rou nding error bound for the inner product of two $n$-vectors $x$ and $y$ is $|fl(x^Ty) - x^Ty| \\le n u |x|^T|y|$\, where $u$ is the unit roundoff\, and the bound is approximately attainable. This bound provides useful in formation only if $nu < 1$. Yet $nu > 1$ for exascale-size problems solve d in single precision and also for problems of order $n > 2048$ solved in half precision. Standard error bounds for matrix multiplication\, LU facto rization\, and so on\, are equally uninformative in these situations. Yet the supercomputers in the TOP500 are there by virtue of having successfull y solved linear systems of orders up to $10^7$\, and deep learning impleme ntations routinely use half precision with apparent success.\n\nHave we re ached the point where our techniques for analyzing rounding errors\, honed over 70 years of digital computation\, are unable to predict the accurac y of numerical linear algebra computations that are now routine? I will sh ow that the answer is "no": we can understand the behaviour of extreme-sca le and low accuracy computations. The explanation lies in algorithmic desi gn techniques (both new and old) that help to reduce error growth along wi th a new probabilistic approach to rounding error analysis.\n LOCATION:https://researchseminars.org/talk/E-NLA/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Benzi (Scuola Normale Superiore Pisa\, Italy) DTSTART:20200506T140000Z DTEND:20200506T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/3 DESCRIPTION:Title: No nlocal dynamics on networks via fractional graph Laplacians: theory and nu merical methods\nby Michele Benzi (Scuola Normale Superiore Pisa\, Ita ly) as part of E-NLA - Online seminar series on numerical linear algebra\n \n\nAbstract\nNonlocal diffusive dynamics on large\, sparse networks can b e modeled by means of systems of differential equations involving fraction al graph Laplacians. The solution of such systems leads to non-analytic ma trix functions\, due to the singularity of the graph Laplacian. Off-diagon al decay estimates for these and related matrix functions will be presente d\, together with explicit (closed form) expressions for some simple but i mportant examples. The case of directed networks (leading to nonsymmetric Laplacians) will also be discussed.\n\nThe numerical approximation of the dynamics can be implemented by means of Krylov subspace methods. The lack of smoothness of the underlying function suggests the use of rational appr oximation techniques. Some results using a shift-and-invert approach will be presented.\n\nApplications include the efficient exploration of large s patial networks and consensus dynamics in multi-agent systems.\n\nThis is joint work with Daniele Bertaccini (U. of Rome `Tor Vergata’)\, Fabio Du rastante (IAC-CNR)\, and Igor Simunec (Scuola Normale Superiore).\n LOCATION:https://researchseminars.org/talk/E-NLA/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Volker Mehrmann (Technische Universität Berlin\, Germany) DTSTART:20200513T140000Z DTEND:20200513T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/4 DESCRIPTION:Title: Ro bustness of linear algebra properties for Port-Hamiltonian systems\nby Volker Mehrmann (Technische Universität Berlin\, Germany) as part of E-N LA - Online seminar series on numerical linear algebra\n\n\nAbstract\nPort -Hamiltonian systems are an important class of control systems that arise in all areas of science and engineering. When the system is linearized aro und a stationary solution one gets a linear port-Hamiltonian system. Despi te the fact that the system looks unstructured at first sight\, it has rem arkable properties. Stability and passivity are automatic\, spectral stru ctures for purely imaginary eigenvalues\, eigenvalues at infinity\, and ev en singular blocks in the Kronecker canonical form are very restricted and furthermore the structure leads to fast and efficient iterative solution methods for associated linear systems. When port-Hamiltonian systems are s ubject to (structured) perturbations\, then it is important to determine t he minimal allowed perturbations so that these properties are not preserve d. The computation of these structured distances to instability\, non-pass ivity\, or non-regularity\, is typically a very hard optimization problem. However\, in the context of port-Hamiltonian systems\, the computation be comes much easier and can even be implemented efficiently for large scale problems in combination with model reduction techniques. We will discuss t hese distances and the computational methods and illustrate the results vi a an industrial problem in the context of noise reduction for disk brakes. \n LOCATION:https://researchseminars.org/talk/E-NLA/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilse Ipsen (North Carolina State University\, USA) DTSTART:20200520T140000Z DTEND:20200520T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/5 DESCRIPTION:Title: Pr obabilistic numerical linear solvers\nby Ilse Ipsen (North Carolina St ate University\, USA) as part of E-NLA - Online seminar series on numerica l linear algebra\n\n\nAbstract\nWe formulate iterative methods for the sol ution of nonsingular linear systems as statistical inference processes by modeling the epistemic uncertainty in the iterates due to a limited comput ational budget. The goal is to obtain well-calibrated uncertainty that is more insightful than traditional worst-case bounds\, and to produce a pr obabilistic description of the error that can be propagated coherently thr ough a computational pipeline.\n\nOur Bayesian Conjugate Gradient Method ( BayesCG) for real symmetric positive-definite linear systems posits a prio r distribution for the solution\, and conditions on the finite amount of i nformation obtained during the iterations to produce a posterior distribu tion that reflects the reduced uncertainty. The following topics will be addressed: (i) choice of prior for fast convergence and well-calibrated u ncertainty\; (ii) error estimation through test statistics that mitigate t he effect of BayesCG's nonlinear dependence on the solution\; and (iii) nu merical stability to maintain positive semi-definiteness of the posteriors \, and prevent convergence slow down from loss of orthogonality in residua ls and search directions.\n\nThis is joint work with Jon Cockayne (http:// www.joncockayne.com/)\, Chris J. Oates (http://oates.work/)\, and Timothy W. Reid (https://math.sciences.ncsu.edu/people/twreid/).\n LOCATION:https://researchseminars.org/talk/E-NLA/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Cleve Moler (MathWorks\, Inc.) DTSTART:20200527T140000Z DTEND:20200527T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/6 DESCRIPTION:Title: Th e Evolution of "The Evolution of MATLAB"\nby Cleve Moler (MathWorks\, Inc.) as part of E-NLA - Online seminar series on numerical linear algebra \n\n\nAbstract\nWe show how MATLAB has evolved over more than 40 years fro m a simple matrix calculator to a powerful technical computing environment . We demonstrate several examples of MATLAB applications. We conclude wit h a discussion of current developments\, including machine learning\, auto mated driving and parallel computation.\n LOCATION:https://researchseminars.org/talk/E-NLA/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Trefethen (University of Oxford) DTSTART:20200603T140000Z DTEND:20200603T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/7 DESCRIPTION:Title: Va ndermonde with Arnoldi\nby Nick Trefethen (University of Oxford) as pa rt of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbstr act\nVandermonde matrices are exponentially ill-conditioned\, rendering th e familiar “polyval(polyfit)” algorithm for polynomial interpolation a nd least-squares fitting ineffective at higher degrees. We show that Arnol di orthogonalization fixes the problem.\n\nIt's remarkable how widely this trick is applicable. Half a dozen examples will be presented.\n\nThis is joint work with Pablo Brubeck and Yuji Nakatsukasa.\n LOCATION:https://researchseminars.org/talk/E-NLA/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Gander (University of Geneva) DTSTART:20200610T140000Z DTEND:20200610T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/8 DESCRIPTION:Title: A Linear Algebra Approach to Time Parallelization: Parareal\, ParaExp\, Para Diag\, ParaOpt and ParaStieltjes\nby Martin Gander (University of Gene va) as part of E-NLA - Online seminar series on numerical linear algebra\n \n\nAbstract\nTime parallelization has been a very active research area ov er the past decade. This is due to so massively parallel computer architec tures that parallelization in the spatial direction rarely suffices to tak e full advantage of such systems when solving evolution problems. Time par allelization is however quite different from spatial parallelization\, sin ce information only propagates forward in time\, never backward. Time para llelization algorithms are often derived at the PDE level\, but whenever t hey are used\, they take the form of solvers for linear algebra problems. I will give in my presentation an introduction to such algorithms at the l inear algebra level\, starting with two simple but typical model problems\ , namely a heat equation and a transport equation. At the linear algebra l evel\, these two problems look deceivingly similar\, but time parallel alg orithms need different features when solving one or the other in parallel. I will explain the reason for this at the linear algebra level\, and then show how Parareal\, ParaExp and ParaDiag address them. If time permits\, I will also briefly explain the newer classes of ParaOpt and ParaStieltjes algorithms.\n LOCATION:https://researchseminars.org/talk/E-NLA/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Embree (Virginia Tech) DTSTART:20200617T140000Z DTEND:20200617T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/9 DESCRIPTION:Title: Co ntour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theory Perspective\nby Mark Embree (Virginia Tech) as part of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbstract\nContour integra l methods for nonlinear eigenvalue problems seek to compute a subset of th e spectrum in a bounded region of the complex plane. We briefly survey thi s class of algorithms\, establishing a relationship to system realization techniques in control theory. This connection motivates new contour integr al methods that build on recent developments in rational interpolation of dynamical systems. The resulting techniques\, which replace the usual Hank el matrices with Loewner matrix pencils\, incorporate general interpolati on schemes and permit ready recovery of eigenvectors. Numerical examples illustrate the potential of this approach.\n\nThis talk describes joint wo rk with Michael Brennan (MIT) and Serkan Gugercin (Virginia Tech).\n LOCATION:https://researchseminars.org/talk/E-NLA/9/ END:VEVENT BEGIN:VEVENT SUMMARY:James Demmel (University of California at Berkeley) DTSTART:20200624T140000Z DTEND:20200624T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/10 DESCRIPTION:Title: C ommunication-Avoiding Algorithms for Linear Algebra\, Machine Learning\, a nd Beyond\nby James Demmel (University of California at Berkeley) as p art of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbst ract\nAlgorithms have two costs: arithmetic and communication\, i.e. movin g data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already gre atly exceed arithmetic costs\, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present new algorithms that communicate asymptotically l ess than their classical counterparts\, for a variety of linear algebra an d machine learning problems\, demonstrating large speedups on a variety of architectures. Some of these algorithms attain provable lower bounds on c ommunication. We describe generalizations of these bounds\, and optimal al gorithms\, to arbitrary code that can be expressed as nested loops accessi ng arrays\, and to account for arrays having different precisions.\n LOCATION:https://researchseminars.org/talk/E-NLA/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Tamara G. Kolda (Sandia National Laboratories) DTSTART:20200701T140000Z DTEND:20200701T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/11 DESCRIPTION:Title: P ractical Leverage-Based Sampling for Low-Rank Tensor Decomposition\nby Tamara G. Kolda (Sandia National Laboratories) as part of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbstract\nConventional alg orithms for finding low-rank canonical polyadic (CP) tensor decompositions are unwieldy for large sparse tensors. The CP decomposition can be comput ed by solving a sequence of overdetermined least problems with special Kha tri-Rao structure. In this work\, we present an application of randomized algorithms to fitting the CP decomposition of sparse tensors\, solving a s ignificantly smaller sampled least squares problem at each iteration with probabilistic guarantees on the approximation errors. Prior work has shown that sketching is effective in the dense case\, but the prior approach ca nnot be applied to the sparse case because a fast Johnson-Lindenstrauss tr ansform (e.g.\, using a fast Fourier transform) must be applied in each mo de\, causing the sparse tensor to become dense. Instead\, we perform sketc hing through leverage score sampling\, crucially relying on the fact that the structure of the Khatri-Rao product allows sampling from overestimates of the leverage scores without forming the full product or the correspond ing probabilities. Naïve application of leverage score sampling is ineffe ctive because we often have cases where a few scores are quite large\, so we propose a novel hybrid of deterministic and random leverage-score sampl ing which consistently yields improved fits. Numerical results on real-wor ld large-scale tensors show the method is significantly faster than compet ing methods without sacrificing accuracy. This is joint work with Brett L arsen\, Stanford University.\n LOCATION:https://researchseminars.org/talk/E-NLA/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Grigori (INRIA Paris) DTSTART:20200708T140000Z DTEND:20200708T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/12 DESCRIPTION:Title: C ommunication avoiding low rank matrix approximation\, an unified perspecti ve on deterministic and randomized approaches\nby Laura Grigori (INRIA Paris) as part of E-NLA - Online seminar series on numerical linear algeb ra\n\n\nAbstract\nIn this talk we present an unified perspective on determ inistic and randomized approaches for computing the low rank approximation of a matrix. We survey recent approaches that allow to minimize communica tion and discuss a generalized LU factorization that allows to unify sever al existing algorithms. For this factorization we present an improved anal ysis which combines deterministic guarantees with sketching ensembles sati sfying Johnson-Lindenstrauss properties. We then extend some of the algori thms to computing the low rank approximation of a tensor by using HOSVD wh ile also avoiding communication.\n LOCATION:https://researchseminars.org/talk/E-NLA/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Lubich (University of Tübingen) DTSTART:20200715T140000Z DTEND:20200715T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/13 DESCRIPTION:Title: D ynamical low-rank approximation\nby Christian Lubich (University of T übingen) as part of E-NLA - Online seminar series on numerical linear alg ebra\n\n\nAbstract\nThis talk reviews differential equations and their num erical solution on manifolds of low-rank matrices or of tensors with a ran k structure such as tensor trains or general tree tensor networks. These l ow-rank differential equations serve to approximate\, in a data-compressed format\, large time-dependent matrices and tensors or multivariate functi ons that are either given explicitly via their increments or are unknown s olutions to high-dimensional evolutionary differential equations\, with mu lti-particle time-dependent Schrödinger equations and kinetic equations s uch as Vlasov equations as noteworthy examples of applications.\n\nRecentl y developed numerical time integrators are based on splitting the project ion onto the tangent space of the low-rank manifold at the current approxi mation. In contrast to all standard integrators\, these projector-splittin g methods are robust to the unavoidable presence of small singular values in the low-rank approximation. This robustness relies on exploiting geomet ric properties of the manifold of low-rank matrices or tensors: in each su bstep of the projector-splitting algorithm\, the approximation moves along a flat subspace of the low-rank manifold. In this way\, high curvature du e to small singular values does no harm.\n\nThis talk is based on work don e intermittently over the last decade with Othmar Koch\, Bart Vandereycken \, Ivan Oseledets\, Emil Kieri\, Hanna Walach and Gianluca Ceruti.\n LOCATION:https://researchseminars.org/talk/E-NLA/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Ng (University of Hong Kong) DTSTART:20200722T140000Z DTEND:20200722T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/14 DESCRIPTION:Title: N onnegative low rank matrix approximation and its applications\nby Mich ael Ng (University of Hong Kong) as part of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbstract\nIn this talk\, we study low ran k matrix approximation (NLRM) for nonnegative matrices arising from many d ata mining and pattern recognition applications. Our approach is different from classical nonnegative matrix factorization (NMF) which has been stud ied for some time. For a given nonnegative matrix\, the usual NMF approach is to determine two nonnegative low rank matrices such that the distance between their product and the given nonnegative matrix is as small as poss ible. However\, the proposed NLRM approach is to determine a nonnegative l ow rank matrix such that the distance between such matrix and the given no nnegative matrix is as small as possible. There are two advantages. (i) Th e minimized distance can be smaller. (ii) The proposed method can identify important singular basis vectors\, while this information may not be obta ined in the classical NMF. Numerical results are reported to demonstrate t he performance of the proposed method. Several extensions and research wor ks are also presented.\n\nThis talk describes joint work with Tai-Xiang Ji ang (Southwestern University of Finance and Economics)\, JunJun Pan (Unive rsite de Mons)\, Guang-Jing Song (Weifang University) and Hong Zhu (Jiangs u University).\n LOCATION:https://researchseminars.org/talk/E-NLA/14/ END:VEVENT BEGIN:VEVENT SUMMARY:David Keyes (KAUST) DTSTART:20200909T140000Z DTEND:20200909T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/15 DESCRIPTION:Title: D ata-sparse Linear Algebra Algorithms for Large-scale Applications on Emerg ing Architectures\nby David Keyes (KAUST) as part of E-NLA - Online se minar series on numerical linear algebra\n\n\nAbstract\nA traditional goal of algorithmic optimality\, squeezing out operations\, has been supersede d because of evolution in architecture. Algorithms must now squeeze memory \, data transfers\, and synchronizations\, while extra operations on local ly cached data cost relatively little time or energy. Hierarchically low-r ank matrices realize a rarely achieved combination of optimal storage comp lexity and high-computational intensity in approximating a wide class of f ormally dense operators that arise in exascale applications. They may be r egarded as algebraic generalizations of the fast multipole method. Methods based on hierarchical tree-based data structures and their simpler cousin s\, tile low-rank matrices\, are well suited for early exascale architectu res\, which are provisioned for high processing power relative to memory c apacity and memory bandwidth. These data-sparse algorithms are ushering in a renaissance of numerical linear algebra. We describe modules of a softw are toolkit\, Hierarchical Computations on Manycore Architectures (HiCMA)\ , that illustrate these features on several applications. Early modules of this open-source project are distributed in software libraries of major v endors. A recent addition\, H2Opus\, extends H2 hierarchical matrix operat ions to distributed memory and GPUs.\n LOCATION:https://researchseminars.org/talk/E-NLA/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisabeth Ullmann (TU Munich) DTSTART:20200916T140000Z DTEND:20200916T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/16 DESCRIPTION:Title: A pproximation of parametric covariance matrices\nby Elisabeth Ullmann ( TU Munich) as part of E-NLA - Online seminar series on numerical linear al gebra\n\n\nAbstract\nCovariance operators model the spatial\, temporal or other correlation between collections of random variables. In modern appli cations these random variables are often associated with an infinite-dimen sional or high-dimensional function space. Examples are the solution of a partial differential equation with random coefficients in uncertainty quan tification (UQ)\, or Gaussian process regression in machine learning. When a suitable discretization of the function space has been applied\, the di scretized covariance operator becomes a very large matrix - the covariance matrix - with a size that is of the order of the dimension of the discret e space squared.\n\nCovariance matrices are naturally symmetric and positi ve semi-definite\, but in the applications we are interested in\, they are typically dense. To avoid the enormous cost of creating and handling thes e dense matrices\, efficient low-rank approximations such as the pivoted C holesky decomposition\, or the adaptive cross approximation (ACA) have bee n developed during the last decade.\n\nBut the story does not end here sin ce recently\, the attention has shifted to parameterized covariance operat ors. This is due to their increased modeling capacity\, e.g.\, in Bayesian inverse problems or Gaussian process regression with hyperparameters in m achine learning. Now we are faced with the task to approximate a parametri c covariance matrix where the parameter itself is a random process. Simply repeating the ACA or pivoted Cholesky decomposition for different paramet er values is inefficient and most certainly too expensive in practise.\n\n We introduce and study two algorithms for the approximation of parametric families of covariance matrices. The first approach is a (non-certified) a pproximation\, and employs a reduced basis associated with a collection of eigenvectors for specific parameter values. The second approach is a cert ified extension of the ACA where the approximation error is controlled in the Wasserstein-2 distance of two Gaussian measures. Both approaches rely on an affine linear expansion of the covariance operator with respect to t he parameter. This keeps the computational cost under control. Notably\, b oth algorithms do not require regular meshes in the covariance operator di scretization and can be used on irregular domains.\n\nThis talk describes joint work with Daniel Kressner (EPFL)\, Jonas Latz (University of Cambrid ge)\, Stefano Massei (TU/e) and Marvin Eisenberger (TUM).\n LOCATION:https://researchseminars.org/talk/E-NLA/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Howard Elman (University of Maryland) DTSTART:20200930T140000Z DTEND:20200930T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/17 DESCRIPTION:Title: M ultigrid Methods for Computing Low-Rank Solutions to Parameter-Dependent P artial Differential Equations\nby Howard Elman (University of Maryland ) as part of E-NLA - Online seminar series on numerical linear algebra\n\n \nAbstract\nThe collection of solutions of discrete parameter-dependent pa rtial differential equations often takes the form of a low-rank matrix. We show that in this scenario\, iterative algorithms for computing these sol utions can take advantage of low-rank structure to reduce both computation al effort and memory requirements. Implementation of such solvers requires that explicit rank-compression computations be done to truncate the ranks of intermediate quantities that must be computed. We prove that when trun cation strategies are used as part of a multigrid solver\, the resulting a lgorithms retain "textbook" (grid-independent) convergence rates\, and we demonstrate how the truncation criteria affect convergence behavior. In ad dition\, we show that these techniques can be used to construct efficient solution algorithms for computing the eigenvalues of parameter-dependent o perators. In this setting\, parameterized eigenvectors can be grouped into matrices of low-rank structure\, and we introduce a variant of inverse su bspace iteration for computing them. We demonstrate the utility of this a pproach on two benchmark problems\, a stochastic diffusion problem with so me poorly separated eigenvalues\, and an operator derived from a discrete Stokes problem whose minimal eigenvalue is related to the inf-sup stabilit y constant.\n\nThis is joint work with Tengfei Su.\n LOCATION:https://researchseminars.org/talk/E-NLA/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Sherry Li (Lawrence Berkeley National Laboratory) DTSTART:20201014T140000Z DTEND:20201014T150000Z DTSTAMP:20260422T225841Z UID:E-NLA/18 DESCRIPTION:Title: A utotuning exascale applications with Gaussian process regression\nby S herry Li (Lawrence Berkeley National Laboratory) as part of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbstract\nSignificant eff ort has been invested to develop highly scalable numerical libraries and h igh-fidelity modeling and simulation for the upcoming exascale computers. These codes typically involve many parameters which need to be selected pr operly to optimize performance on the underlying parallel machine. They ar e also expensive to run and thus have limited "function evaluation" values \, which post significant challenges to efficient performance tuning on di verse architectures.\n\nBayesian optimization with Gaussian process regres sion is an attractive machine learning framework to build surrogate models with limited function evaluation points. In order to fully utilize all th e available data\, we leverage multitask learning and multi-armed bandit s trategies to build a more advanced Bayesian optimization framework.\n\nWe have developed an open-source software tool\, called GPTune\, for optimizi ng expensive large-scale HPC codes. We will show several features of GPTun e\, e.g.\, incorporation of coarse performance models to improve the Bayes ian model\, multi-objective tuning such as tuning a hybrid of time\, memor y and accuracy\, and reuse of historical data base for model portability.\ n\nWe will demonstrate the efficiency and effectiveness of GPTune when it is applied to numerical linear algebra libraries\, such as ScaLAPACK\, Sup erLU and Hypre\, as well as fusion simulation codes M3D-C1 and NIMROD.\n\n This talk describes joint work with James Demmel\, Yang Liu\, Osni Marques \, Wissam Sid-Lakhdar and Xianran Zhu\n LOCATION:https://researchseminars.org/talk/E-NLA/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuji Nakatsukasa (University of Oxford) DTSTART:20201028T150000Z DTEND:20201028T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/19 DESCRIPTION:Title: F ast and stable randomized low-rank matrix approximation\nby Yuji Nakat sukasa (University of Oxford) as part of E-NLA - Online seminar series on numerical linear algebra\n\n\nAbstract\nRandomized SVD has become an extre mely successful approach for efficiently computing a low-rank approximatio n of matrices. In particular the paper by Halko\, Martinsson\, and Tropp ( SIREV 2011) contains extensive analysis\, and has made it a very popular m ethod. The typical complexity for a rank-r approximation of mxn matrices i s O(mnlog n+(m+n)r^2) for dense matrices. The classical Nystrom method is much faster\, but only applicable to positive semidefinite matrices. This work studies a generalization of Nystrom's method applicable to general ma trices\, and shows that (i) it has near-optimal approximation quality comp arable to competing methods\, (ii) the computational cost is the near-opti mal O(mnlog n+r^3) for dense matrices\, with small hidden constants\, and (iii) crucially\, it can be implemented in a numerically stable fashion de spite the presence of an ill-conditioned pseudoinverse. Numerical experime nts illustrate that generalized Nystrom can significantly outperform state -of-the-art methods\, especially when r>>1\, achieving up to a 10-fold spe edup. The method is also well suited to updating and downdating the matrix .\n LOCATION:https://researchseminars.org/talk/E-NLA/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Des Higham (University of Edinburgh) DTSTART:20201111T150000Z DTEND:20201111T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/20 DESCRIPTION:Title: C oncepts and Algorithms for Higher Order Networks: Beyond Pairwise Interact ions\nby Des Higham (University of Edinburgh) as part of E-NLA - Onlin e seminar series on numerical linear algebra\n\n\nAbstract\nNetwork scient ists have shown that there is great value in studying pairwise interaction s between components in a system. From a linear algebra point of view\, th is involves defining and evaluating functions of the associated adjacency matrix. Recently\, there has been increased interest in the idea of accoun ting directly for higher order features. Such features may be built from t he adjacency matrix---for example\, a triangle involving nodes i\, j and k arises when the three edges\, i<->j\, j<->k and k<->i are present. In oth er contexts\, higher order information appears explicitly---for example\, in a coauthorship network\, a document involving three authors forms a nat ural triangle. I will discuss the use of tensor-based definitions and algo rithms to exploit such higher order information. The algorithms also incor porate nonlinearities that increase flexibility. I will focus on spectral methods that extend classical concepts of node centrality and clustering coefficients. The underlying object of study will be a constrained nonline ar eigenvalue problem associated with a tensor. Using recent results from nonlinear Perron--Frobenius theory\, we can establish existence and unique ness under mild conditions\, and show that such spectral measures can be c omputed efficiently and robustly with a nonlinear power method.\n\nThe tal k is based on joint work with Francesca Arrigo (University of Strathclyde) and Francesco Tudisco (Gran Sasso Science Institute).\n LOCATION:https://researchseminars.org/talk/E-NLA/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Francoise Tisseur (Manchester University) DTSTART:20201125T150000Z DTEND:20201125T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/21 DESCRIPTION:by Francoise Tisseur (Manchester University) as part of E-NLA - Online seminar series on numerical linear algebra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Chen Greif (The University of British Columbia) DTSTART:20201209T150000Z DTEND:20201209T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/22 DESCRIPTION:by Chen Greif (The University of British Columbia) as part of E-NLA - Online seminar series on numerical linear algebra\n\nAbstract: TBA \n LOCATION:https://researchseminars.org/talk/E-NLA/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Greenbaum (University of Washington) DTSTART:20210113T150000Z DTEND:20210113T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/23 DESCRIPTION:Title: S pectral Sets: Numerical Range and Beyond\nby Anne Greenbaum (Universit y of Washington) as part of E-NLA - Online seminar series on numerical lin ear algebra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Gillis (University of Mons) DTSTART:20210127T150000Z DTEND:20210127T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/24 DESCRIPTION:Title: I dentifiability and Computation of Nonnegative Matrix Factorizations\nb y Nicolas Gillis (University of Mons) as part of E-NLA - Online seminar se ries on numerical linear algebra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Nagy (Emory University) DTSTART:20210210T150000Z DTEND:20210210T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/25 DESCRIPTION:Title: K rylov Subspace Regularization for Inverse Problems\nby Jim Nagy (Emory University) as part of E-NLA - Online seminar series on numerical linear algebra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Erin Carson (Charles University) DTSTART:20210224T150000Z DTEND:20210224T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/26 DESCRIPTION:Title: W hat do we know about block Gram-Schmidt?\nby Erin Carson (Charles Univ ersity) as part of E-NLA - Online seminar series on numerical linear algeb ra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Gunnar Martinsson (UT Austin) DTSTART:20210310T150000Z DTEND:20210310T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/27 DESCRIPTION:by Gunnar Martinsson (UT Austin) as part of E-NLA - Online sem inar series on numerical linear algebra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Cameron Musco (University of Massachusetts Amherst) DTSTART:20210324T150000Z DTEND:20210324T160000Z DTSTAMP:20260422T225841Z UID:E-NLA/28 DESCRIPTION:Title: H utch++: Optimal Stochastic Trace Estimation\nby Cameron Musco (Univers ity of Massachusetts Amherst) as part of E-NLA - Online seminar series on numerical linear algebra\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/E-NLA/28/ END:VEVENT END:VCALENDAR