试探算法与SSOR预处理共轭梯度算法的拟最佳因子

1引言在求解系数矩阵为对称正定的大型线性代数方程组Au=b (1．1)的迭代法方面,七十年代以来发展了各种预处理共轭梯度法．由于SSOR分裂中具有对称因子,可用于加速共轭梯度法,称为SSOR预处理共轭梯度法(简记为;SSORPCG．同时,由于当松弛因子ω∈(0,2)时,SSOR迭代法收敛,从而进一步发展了m步SSOR预处理共轭梯度法(简记为:m-step SSORPCG．胡家赣证明,经过最优的SSOR预条件,预优     

可行逐步二次规划方法解非线性方程组

We transform the system of nonlinear equations into a nonlinear programming problem, which is attacked by feasible sequential quadratic programming(FSQP) method.We do not employ standard least square approach.We divide the equations into two groups. One group, which contains the equations with zero residual,is treated as equality constraints. The square of other equations is regarded as objective function. Two groups are updated in every step.Therefore, the subproblem is updated at every step, which avoids the difficulty that it is required to lie in feasible region for FSQP.