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 a...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.展开更多
文摘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.
