Publications associées à Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Robust Differentiable SVD

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Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

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

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

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Recursive blocked algorithms for linear systems with Kronecker product structure

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Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to higher-dimensional variants of g ...

SPRINGER2020

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Kathryn Dianne Lund

We analyze an expansion of the generalized block Krylov subspace framework of [Electron.\ Trans.\ Numer.\ Anal., 47 (2017), pp. 100-126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and con ...

MATHICSE2019

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

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A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

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T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

,

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices

Marco Mazza, Stefano Massei

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MATHICSE2018

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

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We consider a family of multivariate trace inequalities recently derived by Sutter, Berta, and Tomamichel. These inequalities generalize the Golden-Thompson inequality and Lieb’s triple matrix inequality to an arbitrary number of matrices in a way that fea ...

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Fast hierarchical solvers for symmetric eigenvalue problems

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In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

MATHICSE Technical Report : Incremental computation of block triangular matrix exponentials with application to option pricing

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Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

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Robust Differentiable SVD

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

Recursive blocked algorithms for linear systems with Kronecker product structure

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

Fast hierarchical solvers for symmetric eigenvalue problems

MATHICSE Technical Report : Incremental computation of block triangular matrix exponentials with application to option pricing

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Fast hierarchical solvers for symmetric eigenvalue problems

Recursive blocked algorithms for linear systems with Kronecker product structure

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

MATHICSE Technical Report : Incremental computation of block triangular matrix exponentials with application to option pricing

MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

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

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices

On multivariate trace inequalities of Sutter, Berta, and Tomamichel

Robust Differentiable SVD