Concept

Generalized minimal residual method

Related publications (60)

Randomized flexible GMRES with deflated restarting

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...

Springer2024

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Daniel Kressner, Alice Cortinovis

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Tommaso Vanzan

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...

2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems

Fabrizio Minganti

The characterization of open quantum systems is a central and recurring problem for the development of quantum technologies. For time-independent systems, an (often unique) steady state describes the average physics once all the transient processes have fa ...

VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF2022

An Inverse-Filter-Based Method to Locate Partial Discharge Sources in Power Transformers

Marcos Rubinstein, Hamidreza Karami

Partial discharge (PD) occurrence in power transformers can lead to irreparable damage to the power network. In this paper, the inverse filter (IF) method to localize PDs in power transformers is proposed. To the best of the authors’ knowledge, this is the ...

2022

Many-body localization in a fragmented Hilbert space

Loïc Jean Pierre Herviou

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than t ...

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

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2020

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