逆問題のための因数分解法 The Factorization Method for Inverse Problems (Oxford Lecture Series in Mathematics and Its Applications)

Kirsch, Andreas/ Grinberg, Natalia

Oxford University Press（2007/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 216 p.
• 言語 ENG
• 商品コード 9780199213535
• DDC分類 515.35

Full Description

The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Source Method, and the Probe Method).

Contents

Preface ; 1. The Simplest Cases: Dirichlet and Neumann Boundary Conditions ; 2. The Factorization Method for Other Types of Inverse Obstacle Scattering Problems ; 3. The Mixed Boundary Value Problem ; 4. The MUSIC Algorithm and Scattering by an Inhomogenous Medium ; 5. The Factorization method for Maxwell's Equations ; 6. The Factorization Method in Impedance Tomography ; 7. Alternative Sampling and Probe Methods ; Bibliography