Ebook: Wavelet Methods — Elliptic Boundary Value Problems and Control Problems

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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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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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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-5
The General Concept....Pages 6-12
Wavelets....Pages 13-33
Elliptic Boundary Value Problems....Pages 34-68
Least Squares Problems....Pages 69-94
Control Problems....Pages 95-128
Back Matter....Pages 129-141

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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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-5
The General Concept....Pages 6-12
Wavelets....Pages 13-33
Elliptic Boundary Value Problems....Pages 34-68
Least Squares Problems....Pages 69-94
Control Problems....Pages 95-128
Back Matter....Pages 129-141
....