行(列)对称矩阵的LDU分解与Cholesky分解

LDU Factorization and Cholesky Factorization of Row (Column) Symmetric Matrices

提出行(列)转置矩阵与行(列)对称矩阵的概念,研究它们的性质,获得一些新的结果.给出行(列)对称矩阵的LDU分解、Cholesky分解和三对角分解公式,可极大地减少行(列)对称矩阵的LDU分解、Cholesky分解和三对角分解的计算量与存储量,而且不会丧失数值精度.

The concept of row （column） transposed matrix and row （column） symmetric matrix are defined. Their basic properties are studied and some new results are obtained. The formula for the LDU factorization, Cholesky factorization and triple diagonal ~actorization of row （column） symmetric matrix are obtained. These formula can dramatically reduce the amount of calculation for LDU factorization, Cholesky factorization and triple diagonal factorization of row （column） symmetric matrix, save dramatically the CPU time and memory without loss of any numerical precision.