Publications related to Iterative refinement of Schur decompositions

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

Florence Graezer Bideau, Huishu Deng

Mega-events have been considered as a strategy to boost urban development, which shifts targets from expansion outside of the original city fabric to reuse of heritage. The bidirectional dynamic between mega-events and heritage has been emphasized, as the ...

2022

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2021

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

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) ...

2021

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

Daniel Kressner, Alice Cortinovis, Marcel Schweitzer

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

SIAM PUBLICATIONS2021

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 ...

2020

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

Felix Schürmann, Bruno Ricardo Da Cunha Magalhães

Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of row ...

2020

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

Daniel Kressner, Stefano Massei

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on linear systems, t ...

SIAM PUBLICATIONS2020

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

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

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Iterative refinement of Schur decompositions

Optimal denoising of rotationally invariant rectangular matrices

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Robust Differentiable SVD

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

A fast spectral divide-and-conquer method for banded matrices

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

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES

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

Graph Chatbot

Chat with Graph Search

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Optimal denoising of rotationally invariant rectangular matrices

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

Robust Differentiable SVD

A fast spectral divide-and-conquer method for banded matrices

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

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

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

Efficient Distributed Transposition Of Large-Scale Multigraphs And High-Cardinality Sparse Matrices

hm-toolbox: MATLAB SOFTWARE FOR HODLR AND HSS MATRICES