一类对称拟定系统的数值方法

Numerical Method for A Class of Symetric Quasi-definite System

证明了对称拟定系统的Schur补问题等价于一个广义最小二乘问题,并基于一种双对角化过程(GKLB过程)推导出了解系统(l)的一种新的迭代算法——LSQR(A(-1),C)方法,该方法不需要求出A和C的Cholesky因子,数值结果表明,与传统的方法(如SYMMLQ方法)比较,该方法有更快的收敛速度。

The Schur complementarity problem of symmetric quasi-definite system is equivalent to a generalized least-squares problem is proved. We can present a new iterative algorithm which named LSQR( A-1,C) method, based on the GKLB process, without needing Cholesky factors of A and C. The numerical results indicate that the algorithm is efficient and converges faster than traditional methods ( SYMMLQ method, etc. ) .