摘要
This paper studies the solutions of symmetric positive definite Toeplitz equations Tx = b by the preconditioned conjugate gradient (PCG ) method. A nuded approach to construct Toeplitz preconditioner is suggested by analysizing the properties of the eigenvalues for various circulant, skewcirculant and sine transform basedmatrices class. Preconditioners developed recently by G.Strang, T.Chan, J.Kuo andT.Huckle, etc., are all special preconditioners in this paper.By adding correctionmatrix to known preconditioner, we suggest using a new preconditioner to obtain abetter approximation in the sense of some norms. Moreover, for generating functionf(x) nonnegative, the proposed sine transform based preconditioner is always effective, this property has overcome the defeault that I.Koltrach, etc.’s sine transformbased preconditioner is invalid in some cases.
This paper studies the solutions of symmetric positive definite Toeplitz equations Tx = b by the preconditioned conjugate gradient (PCG ) method. A nuded approach to construct Toeplitz preconditioner is suggested by analysizing the properties of the eigenvalues for various circulant, skewcirculant and sine transform basedmatrices class. Preconditioners developed recently by G.Strang, T.Chan, J.Kuo andT.Huckle, etc., are all special preconditioners in this paper.By adding correctionmatrix to known preconditioner, we suggest using a new preconditioner to obtain abetter approximation in the sense of some norms. Moreover, for generating functionf(x) nonnegative, the proposed sine transform based preconditioner is always effective, this property has overcome the defeault that I.Koltrach, etc.'s sine transformbased preconditioner is invalid in some cases.
出处
《计算数学》
CSCD
北大核心
1999年第4期451-462,共12页
Mathematica Numerica Sinica
基金
国家自然科学基金!19601012
