Preface
Chapter 1 Introduciton
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 of r(2)F,F(Tmm)and s(2)F,F(Tmm)
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
Chapter9 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