Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /

Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /

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This research monograph deals with applying recently developed wavelet methods to stationary operator equations involving elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions. While wavelets have since their discovery mainly been applied to problems in signal analysis and image compression, their analytic power has also been recognized for problems in Numerical Analysis. Together with the functional analytic framework for differential and integral quations, one has been able to conceptually discuss questions which are relevant for the fast numerical solution of such problems: preconditioning, stable discretizations, compression of full matrices, evaluation of difficult norms, and adaptive refinements. The present text focusses on wavelet methods for elliptic boundary value problems and control problems to show the conceptual strengths of wavelet techniques.

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Main Authors: Kunoth, Angela. author., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: Wiesbaden : Vieweg+Teubner Verlag, 2001
Subjects:Mathematics., Mathematical analysis., Analysis (Mathematics)., Fourier analysis., Applied mathematics., Engineering mathematics., Fourier Analysis., Analysis., Applications of Mathematics.,
Online Access:http://dx.doi.org/10.1007/978-3-322-80027-5
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spelling KOHA-OAI-TEST:2252382018-07-31T00:05:35ZWavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] / Kunoth, Angela. author. SpringerLink (Online service) textWiesbaden : Vieweg+Teubner Verlag,2001.engThis research monograph deals with applying recently developed wavelet methods to stationary operator equations involving elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions. While wavelets have since their discovery mainly been applied to problems in signal analysis and image compression, their analytic power has also been recognized for problems in Numerical Analysis. Together with the functional analytic framework for differential and integral quations, one has been able to conceptually discuss questions which are relevant for the fast numerical solution of such problems: preconditioning, stable discretizations, compression of full matrices, evaluation of difficult norms, and adaptive refinements. The present text focusses on wavelet methods for elliptic boundary value problems and control problems to show the conceptual strengths of wavelet techniques.1 Introduction -- 2 The General Concept -- 3 Wavelets -- 3.1 Preliminaries -- 3.2 Multiscale Decomposition of Function Spaces — Uniform Refinements -- 3.3 Wavelets on an Interval -- 3.4 Wavelets on Manifolds -- 3.5 Multiscale Decomposition of Function Spaces — Non-Uniform Refinements -- 4 Elliptic Boundary Value Problems -- 4.1 General Saddle Point Problems -- 4.2 Elliptic Boundary Value Problems as Saddle Point Problems -- 4.3 Numerical Studies -- 5 Least Squares Problems -- 5.1 Introduction -- 5.2 General Setting -- 5.3 Least Squares Formulation of General Saddle Point Problems -- 5.4 Wavelet Representation of Least Squares Systems -- 5.5 Truncation -- 5.6 Preconditioning and Computational Work -- 5.7 Numerical Experiments -- 6 Control Problems -- 6.1 Introduction -- 6.2 The Continuous Case: Two Coupled Saddle Point Problems -- 6.3 Discretization and Preconditioning -- 6.4 The Discrete Finite—Dimensional Problem -- 6.5 Iterative Methods for WSPP($$ \hat \Lambda ,\Lambda $$) -- 6.6 Alternative Iterative Methods for the Coupled System -- 6.7 Outlook into Nonlinear Problems and Adaptive Strategies -- References.This research monograph deals with applying recently developed wavelet methods to stationary operator equations involving elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions. While wavelets have since their discovery mainly been applied to problems in signal analysis and image compression, their analytic power has also been recognized for problems in Numerical Analysis. Together with the functional analytic framework for differential and integral quations, one has been able to conceptually discuss questions which are relevant for the fast numerical solution of such problems: preconditioning, stable discretizations, compression of full matrices, evaluation of difficult norms, and adaptive refinements. The present text focusses on wavelet methods for elliptic boundary value problems and control problems to show the conceptual strengths of wavelet techniques.Mathematics.Mathematical analysis.Analysis (Mathematics).Fourier analysis.Applied mathematics.Engineering mathematics.Mathematics.Fourier Analysis.Analysis.Applications of Mathematics.Springer eBookshttp://dx.doi.org/10.1007/978-3-322-80027-5URN:ISBN:9783322800275
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Fourier analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Fourier Analysis.
Analysis.
Applications of Mathematics.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Fourier analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Fourier Analysis.
Analysis.
Applications of Mathematics.
spellingShingle Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Fourier analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Fourier Analysis.
Analysis.
Applications of Mathematics.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Fourier analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Fourier Analysis.
Analysis.
Applications of Mathematics.
Kunoth, Angela. author.
SpringerLink (Online service)
Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /
description This research monograph deals with applying recently developed wavelet methods to stationary operator equations involving elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions. While wavelets have since their discovery mainly been applied to problems in signal analysis and image compression, their analytic power has also been recognized for problems in Numerical Analysis. Together with the functional analytic framework for differential and integral quations, one has been able to conceptually discuss questions which are relevant for the fast numerical solution of such problems: preconditioning, stable discretizations, compression of full matrices, evaluation of difficult norms, and adaptive refinements. The present text focusses on wavelet methods for elliptic boundary value problems and control problems to show the conceptual strengths of wavelet techniques.
format Texto
topic_facet Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Fourier analysis.
Applied mathematics.
Engineering mathematics.
Mathematics.
Fourier Analysis.
Analysis.
Applications of Mathematics.
author Kunoth, Angela. author.
SpringerLink (Online service)
author_facet Kunoth, Angela. author.
SpringerLink (Online service)
author_sort Kunoth, Angela. author.
title Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /
title_short Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /
title_full Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /
title_fullStr Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /
title_full_unstemmed Wavelet Methods — Elliptic Boundary Value Problems and Control Problems [electronic resource] /
title_sort wavelet methods — elliptic boundary value problems and control problems [electronic resource] /
publisher Wiesbaden : Vieweg+Teubner Verlag,
publishDate 2001
url http://dx.doi.org/10.1007/978-3-322-80027-5
work_keys_str_mv AT kunothangelaauthor waveletmethodsellipticboundaryvalueproblemsandcontrolproblemselectronicresource
AT springerlinkonlineservice waveletmethodsellipticboundaryvalueproblemsandcontrolproblemselectronicresource
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