Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00520906" target="_blank" >RIV/68145535:_____/20:00520906 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21110/20:00337145 RIV/71226401:_____/20:N0100313
Result on the web
<a href="https://doi.org/10.1137/19M125902X" target="_blank" >https://doi.org/10.1137/19M125902X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M125902X" target="_blank" >10.1137/19M125902X</a>
Alternative languages
Result language
angličtina
Original language name
Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds
Original language description
The paper focuses on numerical solution of parametrized diffusion equations with scalar parameter-dependent coefficient function by the stochastic (spectral) Galerkin method. We study preconditioning of the related discretized problems using preconditioners obtained by modifying the stochastic part of the partial differential equation. We present a simple but general approach for obtaining two-sided bounds to the spectrum of the resulting matrices, based on a particular splitting of the discretized operator. Using this tool and considering the stochastic approximation space formed by classical orthogonal polynomials, we obtain new spectral bounds depending solely on the properties of the coefficient function and the type of the approximation polynomials for several classes of block-diagonal preconditioners. These bounds are guaranteed and applicable to various distributions of parameters. Moreover, the conditions on the parameter-dependent coefficient function are only local, and therefore less restrictive than those usually assumed in the literature.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM/ASA Journal on Uncertainty Quantification
ISSN
2166-2525
e-ISSN
—
Volume of the periodical
8
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
88-113
UT code for WoS article
000551383300004
EID of the result in the Scopus database
2-s2.0-85085289950