系数矩阵为块三对角的线性方程组的并行算法

给出了一种求解系数矩阵为块三对角的线性方程组的适合于ＭＩＭＤ型机的并行算法。从理论上证明了他与ＢＳＯＲ方法有相同的收敛速度，且与块Ｊａｃｏｂｉ方法有相同的并行性，并用一个算例在Ｍｕｌｔｉ－ＴｒａｎｓｐｕｔｅｒＳｙｓｔｅｍ模型机上作了计算，证明了他的有效性与可行性。

An Improved Parallel Algorithm for Solving Linear Equations involving Block Tridiagonal Coefficient Matrix

Yanis's 1990 paper 1] presents a parallel method for solving linear system of equations which involves block tridiagonal coefficient matrix. Ref.1] approximates the level of methods used in P. R. China. But Yanis's method appears to be not sufficiently good in convergence. We now seek to improve convergence without sacrificing parallelism.Conversence is improved through suitable decomposition of matrix A in eq. (1), which represents a system of linear equations. After trying out several likely ways of decomposition, the best is that given by eq. (la). With this best way of decomposition and using the form of the iterative formula of the BSOR method, we establish the needed iterative formula, eq. (2). Then eqs. (3) through (5) are provided for carryins out computation required by our parallel algorithm. Our algorithm is suitable when multi - transputer system is employed as model machine.One illustrative example is given. The times consumed with our parallel algorithm and that of Ref. 1] are respectively 3.347 s and 4.187 s.These results indicate that our algorithm is effective and feasible.