Compress-and-Restart Block Krylov Subspace Methods for Sylvester Matrix Equations

Autor: Kathryn Lund, Davide Palitta, Daniel Kressner, Stefano Massei
Přispěvatelé: Kressner D., Lund K., Massei S., Palitta D., Scientific Computing, Center for Analysis, Scientific Computing & Appl.
Rok vydání: 2021
Předmět:
Sylvester matrix
Polynomial
Iterative method
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
01 natural sciences
low-rank
65F10
65N22
65J10
65F30
65F50
decay
Matrix (mathematics)
linear matrix equation
Compression (functional analysis)
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
FOS: Mathematics
restarts
Applied mathematics
block krylov subspace methods
Mathematics - Numerical Analysis
0101 mathematics
bounds
gmres
Eigenvalues and eigenvectors
Mathematics
Algebra and Number Theory
Applied Mathematics
block Krylov subspace method
Krylov subspace
Numerical Analysis (math.NA)
galerkin
Generalized minimal residual method
large lyapunov
Computer Science::Numerical Analysis
010101 applied mathematics
low-rank compression
numerical-solution
linear matrix equations
projection methods
block Krylov subspace methods
Zdroj: Numerical Linear Algebra and Applications
Numerical Linear Algebra with Applications, 28(1):e2339. Wiley
ISSN: 1070-5325
Popis: 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 subspace methods provide a major reduction in iteration counts over polynomial block KSMs, they also require reliable solvers for the coefficient matrices, and these solvers are often iterative methods themselves. It is not hard to devise scenarios in which the available memory, and consequently the dimension of the Krylov subspace, is limited. In such scenarios for linear systems and eigenvalue problems, restarting is a well-explored technique for mitigating memory constraints. In this work, such restarting techniques are applied to polynomial KSMs for matrix equations with a compression step to control the growing rank of the residual. An error analysis is also performed, leading to heuristics for dynamically adjusting the basis size in each restart cycle. A panel of numerical experiments demonstrates the effectiveness of the new method with respect to extended block KSMs.
Databáze: OpenAIRE
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