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本文提出一个新的高效赛德尔迭代算法(ESI算法)求解大型对称正定稀疏线性方程组AX=b。A是n*n阶的对称正定稀疏系数矩阵。A可表达为A=D+U~T+U,其中D是对角矩阵,U是主对角元素为零的上三角矩阵。这个算法,只需上三角阵非零元及其同等数量的索引信息压缩存储。每行第一个非零元存入界限信息而其他非零元仅需存入对应列号。整个系数矩阵存储量为τ,τ是A的非零元个数。压缩与还原过程仅需O(n)次加法或减法运算。
In this paper, a new efficient Seidel iterative algorithm (ESI algorithm) is proposed to solve the large symmetric positive definite sparse linear system AX = b. A is a n * n order symmetric positive definite sparse coefficient matrix. A can be expressed as A = D + U ~ T + U, where D is the diagonal matrix and U is the upper triangular matrix with zero main diagonal elements. This algorithm, only the triangular array of non-zero element and its equivalent number of index information compression storage. The first non-zero for each line is credited to the limit information and the other nonzero elements need only be stored in the corresponding column number. The whole coefficient matrix storage is τ, τ is the number of non-zero elements of A. Compression and restoration processes require only O (n) additions or subtractions.