Fixed point acceleration iterative algorithm for matrix equation AX+ XB = C

Sylvester matrix equation \boldsymbolAX + \boldsymbolXB = \boldsymbolC is a kind of matrix equation commonly used in numerical algebra research. Aiming at the problem that the calculation effect is not ideal with the increase of matrix size in the solving process, this paper is based on the fixed point iterative algorithm for solving Sylvester matrix equation proposed. The acceleration algorithm of fixed point iteration algorithm is given. At the same time, the convergence of the algorithm is proved and a numerical example is given to illustrate the effectiveness of the algorithm. The experimental results show that the proposed algorithm is faster than the existing iterative algorithm.