CIRCULANT AND SKEWCIRCULANT MATRICES FOR SOLVING TOEPLITZ MATRIX PROBLEMS

作     者：HUCKLE, T 

出 版 物：《SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS》 (工业与应用数学会矩阵分析和应用杂志)

年 卷 期：1992年第13卷第3期

页      面：767-777页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：TOEPLITZ MATRIX CIRCULANT MATRIX PRECONDITIONED CONJUGATE GRADIENT METHOD LANCZOS ALGORITHM RAYLEIGH QUOTIENT ITERATION 

摘      要：In recent papers, numerous authors studied the solutions of symmetric positive definite Toeplitz systems Tx = b by the conjugate gradient method for different families of circulant preconditioners C. In this paper new circulant/skewcirculant approximations are introduced to T and their properties are studied. The main interest is directed to the skewcirculant case. Furthermore, algorithms for computing the eigenvalues of T are formulated, based on the Lanczos algorithm and Rayleigh quotient iteration. For some numerical examples the spectra of C-1 T are compared and the behaviour of the introduced eigenvalue algorithms is displayed.