The Study Of Fast Algorithm For Large Continuous Sylvester Equation AX+XB=F

In this paper,we mainly study the iterative solution of large continuous Sylvester equation AX+XB=F.Firstly,In order to accelerate the convergence rate of the ADI iteration method for solving the Sylvester equation AX+XB=F,we propose two relaxation versions:One is the extrapolation ADI relaxation method(EADI iterative method),and the other is the block super relaxation iterative method(block SORADI iterative method).where the coefficient matrices A and B are assumed to be positive semi-definite matrices(not necessarily Hermitian),and at least one of them to be positive definite.The numerical experiments demonstrate that the EADI iterative method and the block SORADI iterative method have a faster convergence rate than the ADI iteration.In this paper when the coefficient matrices A,B are positive definite Toeplitz matrices,coefficient matrix A and B are split into cyclic anticyclic(CS splitting),and We proposes the CSCS iterative method,derives the convergence theorem and obtains an upper bound of the convergence factor.Numerical experiments show that the CSCS iteration method is more efficient than the SSOR iteration and the HSS iteration method.Finally,in order to improve the convergence rate of CSCS iteration,We further proposes the extrapolated CSCS iteration and analyze its convergence.The numerical experiment results show the effectiveness of the extrapolated CSCS iteration.This thesis consists of four chapters:In Chapter 1,we mainly introduce the research background,the related solution of matrix equations and the innovation point.In Chapter 2,we mainly reviews some basic definitions and theorems frequently used in the sequel.In Chapter 3,we mainly studies the extrapolation ADI iterative method and block SORADI iteration methods for solving the Sylvester equations.In Chapter 4,we mainly studies the cyclic anti-cyclic splitting iterative method for solving the Sylvester equations with Toeplitz Structure.In Chapter 5,we mainly studies the extrapolation cyclic anti-cyclic splitting iterative method for solving the Sylvester equations with Toeplitz Structure.