Toeplitz systems arise in a variety of applications, for instance, numerical differential equations, numerical integral equations of convolut等

●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
●部分目錄

    The use of the preconditioned conjugate gradient method with circulant preconditioners to solve Toeplitz systems was proposed in 1986. In this short book,the author mainly studies some well-known preconditioners from a th等