摘要
A new matrix algebra W, including the set of real symmetric skewcirculant matrices, is introduced. It is proved that all the matrices of W can be simultaneously diagonalized by the discrete W transform matrix. As an application, the use of preconditioned iterative method (preconditioner W1Tn belongs to matrix class W) to solve a system of equations with a Toeplitz coefficients matrix is developed. If generating function f（x） is nonnegative piecewise continuous and has enumerable zero points, we conclude that the spectrum of iterative matrix have a cluster at one. The results of numerical tests with this preconditioner are presented.Our preconditioner is comparable, and if f（x） is not smooth that superior, to Strang’s circulant preconditioner and Huckle’s skewcirculant preconditioner.
A new matrix algebra W, including the set of real symmetric skewcirculant matrices, is introduced. It is proved that all the matrices of W can be simultaneously diagonalized by the discrete W transform matrix. As an application, the use of preconditioned iterative method (preconditioner W1_(T_n) belongs to matrix class W) to solve a system of equations with a Toeplitz coefficients matrix is developed. If generating function f(x) is nonnegative piecewise continuous and has enumerable zero points, we conclude that the spectrum of iterative matrix have a cluster at one. The results of numerical tests with this preconditioner are presented.Our preconditioner is comparable, and if f(x) is not smooth that superior, to Strang's circulant preconditioner and Huckle's skewcirculant preconditioner.
出处
《计算数学》
CSCD
北大核心
2000年第1期73-82,共10页
Mathematica Numerica Sinica
基金
国家自然科学基金!(19601012)
