论文标题
扩展循环还原算法的理论分析
Theoretical analysis of the extended cyclic reduction algorithm
论文作者
论文摘要
Swarztrauber在1974年开发的扩展循环还原算法用于求解块 - tridiagonal线性系统。该论文填补了有关矩阵多项式$ b_ {i}^{（r）} $的理论结果的空白，相对于三角矩阵，这是由牛顿在扩展的环状还原算法中在牛顿方法计算的。同时，研究了用于求解块 - 三角对的扩展循环还原算法的正向误差分析。为了实现这两个目标，关键点是找出矩阵多项式$ b_ {i}^{（r）} $的零是系数矩阵的主要子矩阵的特征值。
The extended cyclic reduction algorithm developed by Swarztrauber in 1974 was used to solve the block-tridiagonal linear system. The paper fills in the gap of theoretical results concerning the zeros of matrix polynomial $B_{i}^{(r)}$ with respect to a tridiagonal matrix which are computed by Newton's method in the extended cyclic reduction algorithm. Meanwhile, the forward error analysis of the extended cyclic reduction algorithm for solving the block-tridiagonal system is studied. To achieve the two aims, the critical point is to find out that the zeros of matrix polynomial $B_{i}^{(r)}$ are eigenvalues of a principal submatrix of the coefficient matrix.
