linear algebra 1 epfl

• Publications

Linear algebra

General information.

John H. Maddocks --> John H. Maddocks

Lectures: Tuesday 21.9.2021 at 13h15 - 15h00, room CO2       Each Thursday 14h15 - 16h00, room CE3

Principal assistant:

Harmeet Singh

• Important Notes:
• Polycopiés
• Notes of the course by prof. J. Descloux
• Notes of the course by prof. C. A. Stuart: part I and part II

In addition to learning the material, you need to start to learn how to read descriptions of the same material from slightly different point of view. The two polycopiés are deliberately two different perspectives. The course is a third viewpoint, in between.

• Linear Algebra and its Applications, D.C. Lay, Pearson (5th edition).

Contents of part I

• Announcements

Check here for any announcements about the course.

A revision session will take place Thursday 11th January from 10h to 12h in CE 5

!!! A revision session is organised Friday 13th January 2017 from 10h to 12h in CE 5 !!!

• Week-by-week correspondence
• Requirements
• Integration over 1, 2, and 3-dimensional domains
• Change of variables in 1, 2, and 3-dimensional domains
• Integration by parts in 1 dimensional integrals
• Chain rule for partial derivatives
• Back to top

Online People Directory

Daniel kressner.

Full Professor

[email protected] +41 21 693 25 46 http://anchp.epfl.ch

EPFL SB MATH ANCHP MA B2 514 (Bâtiment MA) Station 8 1015 Lausanne

+41 21 693 25 46 +41 21 693 25 79 Office:  MA B2 514 EPFL > SB > MATH > ANCHP

Web site:  Web site:  https://anchp.epfl.ch/

+41 21 693 25 46 EPFL > SB > SB-SMA > SMA-ENS

Web site:  Web site:  https://sma.epfl.ch/

+41 21 693 25 46 EPFL > VPA > VPA-FAC > CEAE

vCard Administrative data

Publications

Infoscience publications, infoscience, certified and fast computations with shallow covariance kernels.

D. Kressner ;  J. Latz ;  S. Massei ;  E. Ullmann

Detailed record

Numerical Mathematics and Control Preface to a Special Issue Dedicated to Volker Mehrmann on the Occasion of his 65th Birthday

P. Benner ;  D. Kressner ;  H. X. Phu

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

D. Kressner ;  K. Lund ;  S. Massei ;  D. Palitta

Recursive blocked algorithms for linear systems with Kronecker product structure

M. Chen ;  D. Kressner

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

A. Cortinovis ;  D. Kressner ;  S. Massei

Low-Rank Approximation In The Frobenius Norm By Column And Row Subset Selection

A. Cortinovis ;  D. Kressner

Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing

K. Glau ;  D. Kressner ;  F. Statti

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

S. Massei ;  L. Robol ;  D. Kressner

MATHICSE Technical Report : Low-rank approximation in the Frobenius norm by column and row subset selection

Mathicse technical report : low-rank updates and divide-andconquer methods for quadratic matrix equations.

D. Kressner ;  P. Kürschner ;  S. Massei

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Numerical methods for option pricing: polynomial approximation and high dimensionality.

F. Statti / D. Kressner ;  D. Filipovic (Dir.)

hm-toolbox: Matlab software for HODLR and HSS matrices

Low-rank updates and a divide-and-conquer method for linear matrix equations.

D. Kressner ;  S. Massei ;  L. Robol

7th Workshop on Matrix Equations and Tensor Techniques

P. Benner ;  H. Fassbender ;  L. Grasedyck ;  D. Kressner ;  B. Meini   et al.

MATHICSE Technical Report : Fast QR decomposition of HODLR matrices

D. Kressner ;  A. Susnjara

MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

A. Susnjara ;  D. Kressner

Multigrid Methods Combined With Low-Rank Approximation For Tensor-Structured Markov Chains

M. Bolten ;  K. Kahl ;  D. Kressner ;  F. Macedo ;  S. Sokolovic

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Z. Bujanovic ;  L. Karlsson ;  D. Kressner

SUBSPACE ACCELERATION FOR THE CRAWFORD NUMBER AND RELATED EIGENVALUE OPTIMIZATION PROBLEMS

D. Kressner ;  D. Lu ;  B. Vandereycken

LOW-RANK UPDATES OF MATRIX FUNCTIONS

B. Beckermann ;  D. Kressner ;  M. Schweitzer

FAST COMPUTATION OF THE MATRIX EXPONENTIAL FOR A TOEPLITZ MATRIX

D. Kressner ;  R. Luce

Fast hierarchical solvers for symmetric eigenvalue problems

A. Susnjara / D. Kressner (Dir.)

Low-rank tensor methods for large Markov chains and forward feature selection methods

F. Santos Paredes Quartin de Macedo / D. Kressner ;  A. M. Pacheco Pires (Dir.)

Distributed Signal Processing via Chebyshev Polynomial Approximation

D. I. Shuman ;  P. Vandergheynst ;  D. Kressner ;  P. Frossard

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

Mathicse technical report : incremental computation of block triangular matrix exponentials with application to option pricing.

D. Kressner ;  R. Luce ;  F. Statti

Recompression Of Hadamard Products Of Tensors In Tucker Format

D. Kressner ;  L. Perisa

Fast Computation Of Spectral Projectors Of Banded Matrices

Structure-preserving low multilinear rank approximation of antisymmetric tensors.

E. Begovic Kovac ;  D. Kressner

Multilevel tensor approximation of PDEs with random data

J. Ballani ;  D. Kressner ;  M. D. Peters

A Novel Iterative Method To Approximate Structured Singular Values

N. Guglielmi ;  M.-U. Rehman ;  D. Kressner

Learning heat diffusion graphs

D. Thanou ;  X. Dong ;  D. Kressner ;  P. Frossard

MATHICSE Technical Report : Fast computation of spectral projectors of banded matrices

Mathicse technical report : perturbation of higher-order singular values.

W. Hackbusch ;  D. Kressner ;  A. Uschmajew

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Mathicse technical report : multilevel tensor approximation of pdes with random data, mathicse technical report : a novel iterative method to approximate structured singular values, mathicse technical report : multigrid methods combined with low-rank approximation for tensor structured markov chains.

M. Bolten ;  K. Kahl ;  D. Kressner ;  F. Santos Paredes Quartin de Macedo ;  S. Sokolović

MATHICSE Technical Report : Structure-preserving low multilinear rank approximation of antisymmetric tensors

E. B. Kovač ;  D. Kressner

Subspace Acceleration For Large-Scale Parameter-Dependent Hermitian Eigenproblems

P. Sirkovic ;  D. Kressner

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

D. Kressner ;  M. Steinlechner ;  B. Vandereycken

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

J. Ballani ;  D. Kressner

Projection Methods For Large-Scale T-Sylvester Equations

F. M. Dopico ;  J. Gonzalez ;  D. Kressner ;  V. Simoncini

Parallel algorithms for tensor completion in the CP format

L. Karlsson ;  D. Kressner ;  A. Uschmajew

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

P. Sirkovic / D. Kressner (Dir.)

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

M. M. Steinlechner / D. Kressner (Dir.)

A block algorithm for computing antitriangular factorizations of symmetric matrices

Z. Bujanovic ;  D. Kressner

On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems

D. Kressner ;  A. Uschmajew

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

F. Bonizzoni ;  F. Nobile ;  D. Kressner

MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

Mathicse technical report : accelerated filtering on graphs using lanczos method.

A. Susnjara ;  N. Perraudin ;  D. Kressner ;  P. Vandergheynst

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

D. Kressner ;  M. M. Steinlechner ;  B. C. Vandereycken

MATHICSE Technical Report : Subspace acceleration for large-scale parameter-dependent Hermitian eigenproblems

Algorithm 953: parallel library software for the multishift qr algorithm with aggressive early deflation.

R. Granat ;  B. Kagstrom ;  D. Kressner ;  M. Shao

Numerical Mathematics and Advanced Applications - ENUMATH 2013

A. Abdulle ;  S. Deparis ;  D. Kressner ;  F. Nobile ;  M. Picasso

Accelerated filtering on graphs using Lanczos method

Truncated low-rank methods for solving general linear matrix equations.

D. Kressner ;  P. Sirkovic

Low rank differential equations for Hamiltonian matrix nearness problems

N. Guglielmi ;  D. Kressner ;  C. Lubich

Adaptive polynomial approximation by means of random discrete least squares

G. Migliorati

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

D. Kressner ;  R. Kumar ;  F. Nobile ;  C. Tobler

MATHICSE Technical Report : Tensor train approximation of moment equations for the log-normal Darcy problem

Mathicse technical report : low-rank tensor approximation for high-order correlation functions of gaussian random fields, a parallel qz algorithm for distributed memory hpc systems.

B. Adlerborn ;  B. Kagstroem ;  D. Kressner

Low-Rank Tensor Methods With Subspace Correction For Symmetric Eigenvalue Problems

D. Kressner ;  M. Steinlechner ;  A. Uschmajew

Low-Rank Tensor Methods for Communicating Markov Processes

D. Kressner ;  F. Macedo

Computing Extremal Points Of Symplectic Pseudospectra And Solving Symplectic Matrix Nearness Problems

On the eigenvalue decay of solutions to operator lyapunov equations.

L. Grubisic ;  D. Kressner

Bivariate Matrix Functions

D. Kressner

Nonlinear Eigenvalue Problems With Specified Eigenvalues

M. Karow ;  D. Kressner ;  E. Mengi

Low-rank tensor completion by Riemannian optimization

Memory-efficient arnoldi algorithms for linearizations of matrix polynomials in chebyshev basis.

D. Kressner ;  J. E. Roman

An indefinite variant of LOBPCG for definite matrix pencils

D. Kressner ;  M. M. Pandur ;  M. Shao

On A Perturbation Bound For Invariant Subspaces Of Matrices

M. Karow ;  D. Kressner

Algorithm 941: htucker-A MATLAB Toolbox for Tensors in Hierarchical Tucker Format

D. Kressner ;  C. Tobler

Generalized eigenvalue problems with specified eigenvalues

D. Kressner ;  E. Mengi ;  I. Nakic ;  N. Truhar

Optimally Packed Chains of Bulges in Multishift QR Algorithms

L. Karlsson ;  D. Kressner ;  B. Lang

Subspace Methods For Computing The Pseudospectral Abscissa And The Stability Radius

D. Kressner ;  B. Vandereycken

Dense and Structured Matrix Computations

M. Shao / D. Kressner ;  B. Kågström (Dir.)

A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations

D. Kressner ;  M. Plesinger ;  C. Tobler

An Error Analysis Of Galerkin Projection Methods For Linear Systems With Tensor Product Structure

B. Beckermann ;  D. Kressner ;  C. Tobler

Structured Canonical Forms For Products Of (Skew-) Symmetric Matrices And The Matrix Equation XAX = B

D. Kressner ;  X. Liu

Robust Solution Methods for Nonlinear Eigenvalue Problems

P. C. Effenberger / D. Kressner (Dir.)

Chebyshev interpolation for nonlinear eigenvalue problems

C. Effenberger ;  D. Kressner

Accelerating Model Reduction of Large Linear Systems with Graphics Processors

P. Benner ;  P. Ezzatti ;  D. Kressner ;  E. Quintana-Orti ;  A. Remon

On aggressive early deflation in parallel variants of the QR algorithm

B. Kagstrom ;  D. Kressner ;  M. Shao

Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems

Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems.

W.-J. Beyn ;  C. Effenberger ;  D. Kressner

Sparsity-seeking fusion of digital elevation models

H. Papasaika ;  E. Kokiopoulou ;  E. Baltsavias ;  K. Schindler ;  D. Kressner

Optimal similarity registration of volumentric images

E. Kokiopoulou ;  D. Kressner ;  M. Zervos ;  N. Paragios

Linear dimension reduction for evolutionary data

E. Kokiopoulou ;  D. Kressner ;  Y. Saad

Bivariate matrix functions

Low-rank tensor krylov subspace methods for parametrized linear systems, linearization techniques for band structure calculations in absorbing photonic crystals.

C. Effenberger ;  D. Kressner ;  C. Engstrom

Structured eigenvalue condition numbers and linearizations for matrix polynomials

B. Adhikari ;  R. Alam ;  D. Kressner

Computing Codimensions And Generic Canonical Forms For Generalized Matrix Products

B. Kagstrom ;  L. Karlsson ;  D. Kressner

A mixed-precision algorithm for the solution of Lyapunov equations on hybrid CPU-GPU platforms

P. Benner ;  P. Ezzatti ;  D. Kressner ;  E. Quintana-Orti ́ ;  A. Remón

Condensed forms for the symmetric eigenvalue problem on multi-threaded architectures

P. Bientinesi ;  F. D. Igual ;  D. Kressner ;  M. Petschow ;  E. S. Quintana-Ortí

Perturbation, extraction and refinement of invariant pairs for matrix polynomials

T. Betcke ;  D. Kressner

Teaching & PhD

Mathematics

PhD Students

Past epfl phd students, advanced linear algebra i, computational linear algebra, numerical linear algebra for koopman and dmd, all postal addresses and positions.

EPFL SB MATH ANCHP Full Professor Status: Staff

EPFL SB SB-SMA SMA-ENS Full Professor Status: Staff

EPFL VPA VPA-FAC CEAE Member Status: Staff

Computational linear algebra

Enrolment options, math-453 computational linear algebra.

• Professor: Daniel Kressner
• Teacher: Hei Yin Lam

Self enrolment (Student)

Campus access (read only).

• EPFL CH-1015 Lausanne
• +41 21 693 11 11

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© 2023 EPFL, all rights reserved

Coursebooks

Computational linear algebra

MATH-496 / 5 credits

Language: English

Remark: pas donné en 2023-24

This is an introductory course to the concentration of measure phenomenon - random functions that depend on many random variables tend to be often close to constant functions.

This course is accessible to motivated 3rd year students.

log-Sobolev inequalities, isoperimetry, entropy

Learning Prerequisites

Required courses.

Mathematics Bachelor's level knowledge of analysis, linear algebra and probability (for example, the Bloc "Science de Base" in EPFL Mathematics Bachelor's program).

Teaching methods

Lectures + exercise classes

Assessment methods

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Bibliography

• R.van Handel's lecture notes on "Probability in high dimension" (available on his webpage)
• "Concentration Inequalities: A Nonasymptotic Theory of Independence" by S. Boucheron, G. Lugosi and P. Massart.

Ressources en bibliothèque

• Concentration Inequalities: A Nonasymptotic Theory of Independence / Boucheron
• Probability in high dimension / Handel van

In the programs

• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Computational linear algebra
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

Reference week

Exercise, TP

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MATH-453: Computational linear algebra

This course provides an overview of advanced techniques for solving large-scale linear algebra problems, as they typically arise in applications. A central goal of this course is to give the ability to choose a suitable solver for a given application.

• https://edu.epfl.ch/coursebook/en/computational-linear-algebra-MATH-453

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