金小慶主編的《塊-特普利茲迭代方法(英文版)
》介紹區組Toeplity方程迭代解法的理論和應用。特
普利茨，德國數學家，生於德國布雷斯勞，早年在布
雷斯勞大學學習，1905年獲博士學位。先後在格丁根
大學、基爾大學、波恩大學工作。特普利茨深人研究
了無窮線性型、雙線性型、二次型以及相伴無限矩陣
等課題，並把所得結果廣泛應用於分析學各領域。他
對算子理論、凸空間理論和發散級數論等方面都頗有
研究。

Preface
Chapter 1 Introduction
1.1 Background
1.2 Circulant preconditioners
1.3 Non-circulant preconditioners
Chapter 2 Block Circulant Preconditioners
2.1 Operators for block matrices
2.2 Operation cost for preconditioned system
2.3 Convergence rate
2.4 Invertibility ofr(2)F,F(Tmn) and 8 (2)F,F(Tmn)
2.5 Numerical results
Chapter 3 BCCB Preconditioners from Kernels
3.1 Introduction
3.2 Preconditioners from kernels
3.3 Clustering properties
Chapter 4 Fast Algorithm for Tensor Structure
4.1 Construction of preconditioner
4.2 Fast algorithm
4.3 Inverse heat problem
4.4 Numerical results
Chapter 5 Block Toeplitz LS Problems
5.1 Introduction
5.2 Construction of preconditioner
5.3 Spectrum of preconditioned matrix
5.4 Convergence rate and operation cost
Chapter 6 Block {ω}-Circulant Preconditioners
6.1 Spectral analysis
6.2 Construction of preconditioner
6.3 Clustering of eigenvalues
6.4 Numerical results
Chapter 7 Non-Circulant Block Preconditioners
7.1 Block band Toeplitz preconditioners
7.2 Preconditioners based on fast transforms
Chapter 8 Multigrid Block Toeplitz Solvers
8.1 Introduction
8.2 Convergence rate of TGM
8.3 Convergence result for full MGM
8.4 Numerical results
Chapter 9 Applications in Second-Order PDEs
9.1 Applications to elliptic problems
9.2 Applications to hyperbolic problems
9.3 Extension to parabolic equations
9.4 Numerical results
9.5 3-dimensional problems
Chapter 10 Applications in First-Order PDEs
10.1 Discretized system and GMRES method
10.2 Construction of preconditioner
10.3 Convergence rate
10.4 Spectral analysis
10.5 Asymptotic properties
10.6 Convergence results and numerical tests
Chapter 11 Applications in ODEs and DAEs
11.1 BVMs and their matrix forms
11.2 Construction of preconditioner
11.3 Convergence rate and operation cost
11.4 Algorithm for DAEs
11.5 Numerical results
Chapter 12 Applications in Image Processing
12.1 Introduction
12.2 Regularized PCGLS method
12.3 Numerical results
Bibliography
Index