Toeplitz系统预处理方法

1 introduction
1.1 background in numerical linear algebra
1.1.1 basic symbols, notations, and definitions
1.1.2 spectral properties of hermitian matrix
1.1.3 norms and condition number
1.2 toeplitz systems
1.3 conjugate gradient method
1.4 gmres method
1.5 basic knowledge of iterative toeplitz solvers
1.5.1 circulant preconditioners
1.5.2 generating function and spectral analysis
2 strang's circulant preconditioner
2.1 introduction
2.2 convergence rate
3 t. chan's optimal preconditioner
3.1 introduction
3.2 convergence rate
3.3 non-circulant optimal preconditioners
3.3.1 optimal sine transform preconditioner
3.3.2 optimal cosine transform preconditioner
3.3.3 optimal hartley transform preconditioner
3.3.4 convergence result and operation cost
3.4 linear operator cu
3.5 stability
4 superoptimal preconditioner
4.1 introduction
4.2 convergence rate
4.3 spectral relation of preconditioned matrices
4.4 numerical results
5 ill-conditioned toeplitz systems
5.1 band-toeplitz preconditioner
5.2 {w}-circulant preconditioner
5.2.1 construction of preconditioner
5.2.2 spectral analysis
6 block preconditioner
6.1 block operator■
6.2 complexity of preconditioned system
6.3 convergence rate
6.4 numerical results
7 application in odes
7.1 background of bvms
7.1.1 linear multistep formulas
7.1.2 block-bvms and their matrix forms
7.2 construction of preconditioner
7.3 convergence rate and operation cost
7.4 numerical results
a m-files used in chapter 7
a.1
a.2
a.3
a.4
a.5
bibliography
index