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.
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机译：进一步开发了限制性预处理共轭梯度（RPCG）方法，以解决块二乘二结构线性方程组的稀疏系统。这种新方法的基本思想是，我们将RPCG方法应用于块2 x 2线性系统的正态残差方程，并通过使用相关矩阵块的不完全正交分解来构造每个所需的近似矩阵。数值实验表明，该新方法被称为正态残差上的限制性预处理共轭梯度（RPCGNR），比已知的RPCG方法或正态残差上的标准共轭梯度（CGNR）方法更可靠，更有效。大型稀疏鞍点问题。
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