一类Krylov子空间方法在求解Sylvester方程的应用

Application of a Kind of Krylov Subspace Methods in Solving the Sylvester Equation

提出了一种求解Sylvester方程AX+XB=EFT的块Krylov子空间方法。当矩阵A和B非常大,并且右侧的的秩很小时,给出如何求解精确低秩近似解。理论结果和数值实例证明了方法的有效性。

Block Krylov subspaee methods for solving the Sylvester matrix equationAX ＋ XB = EFT is proposed. When both matrices A and B are large and the right-hand side matrix is of small rank, it is shown that how to extract low-rank ap- proximations. Some theoretical results are given and numerical experiments show the effectiveness of these block methods.