Iterative Methods Of Large-Scale Matrix Equation A×B=C And Their Applications

The matrix equation AXB=C plays an important role in the field of scientific computation,control theory and engineering.The paper mainly concerns the induced splitting iterative method for matrix equation AXB=C.Firstly,the induced splitting iterative versions for the matrix equation AXB=C and its convergence are studied,when the coefficient matrices A and B are hermitian positive definite matrices or H-matrices.Numerical experiment of surface fitting shows that our method is much more efficient than the traditional progressive iterative approximation(PIA).Secondly,in order to accelerate the convergent rate of the induced splitting iterative method,we have developed an extrapolation method based on the induced splitting iterative method.Numerical experiments show that the extrapolation method and successive over relaxation method have faster convergent rate than induced splitting iterative method.This paper consists of four chapters,the structure is as follows:The first chapter is the introduction,we mainly introduce the research background of matrix equation,research at home and abroad,the currently and some relative methods of the matrix equation,as well as the innovation points of the paper;The second chapter is the preliminary knowledge,we recall some related definitions and theorems used in the sequence of the paper;In the third chapter,we first establish the stationary splitting iterative method for matrix equation AXB=C.Then,we analyze its convergent theorem,preconditioned variants and give some numerical experiments;In the fourth chapter,we research the extrapolation method,analyze its convergent rate and numerical experiment for solving the matrix equation AXB=C.