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 ...
Springer2024SPEEDING 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 Publications2024TimeEvolver: A program for time evolution with improved error bound
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 ...
ELSEVIER2022Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning
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 ...
2022DIVIDE-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 PUBLICATIONS2022Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
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 QUANTENWISSENSCHAF2022An 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 ...
2022Many-body localization in a fragmented Hilbert space
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 ...
2021Low-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 PUBLICATIONS2021A 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