Wavelet Methods - Elliptic Boundary Value Problems and Control Problems : Elliptic Boundary Value Problems and Control Problems (Advances in Numerical Mathematics) （2001. x, 141 S. X, 141 p. 229 mm）

個数：

Wavelet Methods - Elliptic Boundary Value Problems and Control Problems : Elliptic Boundary Value Problems and Control Problems (Advances in Numerical Mathematics) （2001. x, 141 S. X, 141 p. 229 mm）

  • 在庫がございません。海外の書籍取次会社を通じて出版社等からお取り寄せいたします。
    通常6～9週間ほどで発送の見込みですが、商品によってはさらに時間がかかることもございます。
    【重要ご説明事項】
    1. 納期遅延や、ご入手不能となる場合がございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 【入荷遅延について】
    世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
    おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。
  • ◆画像の表紙や帯等は実物とは異なる場合があります。
  • ◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
    また、洋書販売価格は、ご注文確定時点での日本円価格となります。
    ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。
  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 151 p.
  • 言語 ENG
  • 商品コード 9783519003274
  • DDC分類 515

Full Description

While wavelets have since their discovery mainly been applied to problems in signal analysis and image compression, their analytic power has more and more also been recognized for problems in Numerical Analysis. Together with the functional analytic framework for different differential and integral quations, one has been able to conceptu­ ally discuss questions which are relevant for the fast numerical solution of such problems: preconditioning issues, derivation of stable discretizations, compression of fully popu­ lated matrices, evaluation of non-integer or negative norms, and adaptive refinements based on A-posteriori error estimators. This research monograph focusses on applying wavelet methods to elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions. Moreover, a control problem with an elliptic boundary problem as contraint serves as an example to show the conceptual strengths of wavelet techniques for some of the above mentioned issues. At this point, I would like to express my gratitude to several people before and during the process of writing this monograph. Most of all, I wish to thank Prof. Dr. Wolfgang Dahmen to whom I personally owe very much and with whom I have co-authored a large part of my work. He is responsible for the very stimulating and challenging scientific atmosphere at the Institut fiir Geometrie und Praktische Mathematik, RWTH Aachen. We also had an enjoyable collaboration with Prof. Dr. Reinhold Schneider from the Technical University of Chemnitz.

Contents

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.