大型对称变带宽方程组的Cholesky分解法

A CHOLESKY DECOMPOSITION METHOD FOR LARGE-SCALE SYMMETRICAL SYSTEM OF EQUATIONS WITH VARYING BAND WIDTH

作者针对地球物理数值模拟中常碰到的大型稀疏变带宽方程组的求解问题 ,介绍了一种大型稀疏变带宽矩阵的存储方法及 Cholesky分解法。该方法的特点是用二个一维数组 ,其中一个输入时存储对称稀疏矩阵变带宽内的元素 ,输出时存储 Cholesky下三角矩阵带宽内的元素 ;另一个存储对称变带宽矩阵对角线元素在前一维数组中的位置 ,大大节约了所占的计算机内存空间。

In view of the solution of system of linear equations in the geophysical numerical analog, the paper presents a method for storing the large scale spare matrix with varying band width and its cholesky decomposition. Its major feature is to reduce EMS memory allocation greatly by the help of two one dimensional arrays: one is used to deposite the elements within the band width of the matrix at input stage and latter store the elements within the band width of cholesky lower triangle matrix at output stage; another is used to store the locations of diagonal elements of the spare symmetrical matrix in the forenamed one dimensional array.