THE RESTRICTIVELY PRECONDITIONED CONJUGATE GRADIENT METHODS ON NORMAL RESIDUAL FOR BLOCK TWO-BY-TWO LINEAR SYSTEMS

The restrictively preconditioned conjugate gradient （RPCG） method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the restrictively preconditioned conjugate gradient on normal residual （RPCGNR）, is more robust and effective than either the known RPCG method or the standard conjugate gradient on normal residual （CGNR） method when being used for solving the large sparse saddle point problems.

一种新的模糊神经网络删剪策略

模糊规则的数量直接决定模糊神经网络结构的复杂度和效率.基于神经网络自构行学习(NNSCL)算法,用共轭剃度预条件正则方程算法求取删除隐层神经元后的剩余权值,得到改进的NNSCL-1算法.将此算法应用到模糊神经网络的规则推理层,可以极大地优化网络的规则及结构,并且结构优化后不需要重新训练也能保持网络的精确度和泛化能力.仿真结果显示了此算法的有效性和可行性.

一类等式约束优化问题的改进牛顿算法

提出了牛顿方法与预优广义共轭梯度方法相结合的方法(简称为Newton-PGCG)求解库恩-塔克方程组。给出Newton-PGCG算法中预优广义共轭梯度法中预优阵的选取问题及其步数参数的确定原则,并在保证牛顿方法恰二阶收敛的条件下,证明了此算法也具有恰二阶收敛的优点。

解非对称块三对角线性方程组的并行算法

提出了一种并行求解非对称块三对角线性方程组的方法。该方法通过对传统的预处理共轭梯度法的预条件子进行重新构造,使之适合并行计算。该算法只需相邻两台机子间通信,降低了通信次数易于求解。并从理论上分析文中算法的收敛性,给出了该算法的收敛性优于Gauss-seidel的预处理共轭梯度法的充分条件。最后,在HP rx2600集群上,进行了数值试验,结果表明实算与理论是一致的,并行性好,且迭代次数也明显降低。