Krylov Subspace Methods: Principles and Analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00382293" target="_blank" >RIV/67985807:_____/13:00382293 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/13:10126674

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Krylov Subspace Methods: Principles and Analysis

Popis výsledku v původním jazyce

The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterisedby their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments. This allows enlightening reformulations of questions from matrix computations into the languageof orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. T

Název v anglickém jazyce

Krylov Subspace Methods: Principles and Analysis

Popis výsledku anglicky

The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterisedby their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments. This allows enlightening reformulations of questions from matrix computations into the languageof orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. T

Druh

B - Odborná kniha

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

ISBN

978-0-19-965541-0

Počet stran knihy

408

Název nakladatele

Oxford University Press

Místo vydání

Oxford

Kód UT WoS knihy

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