矩阵和的Schur补的性质

摘要

In order to reduce the large-scale matrix calculation and simplify the matrix equation numerical calculation, the properties of Schur complement of the sum of block matrix was studied. The two properties of Schur complement of the sum of block matrix were obtained by the effect of Schur complement with the replacement of block. They were proved in the theory, the theoretical support was provided to deal with the large-scale matrix calculation.%为减少大规模的矩阵计算,简化矩阵方程的数值计算,研究了分块矩阵和的Schur补的性质.通过研究矩阵的分块置换对Schur补的影响,获得分块矩阵和的Schur补的2个性质,并在理论上予以证明,为处理大规模的矩阵计算提供了理论支撑.