SPMR: A Family of Saddle-Point Minimum Residual Solvers
SPMR: A Family of Saddle-Point Minimum Residual Solvers
复制标题
SPMR：鞍点最小残差求解器系列
DOI：
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发表时间：
2018
影响因子：
3.1
通讯作者：
C. Greif
中科院分区：
文献类型：
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作者：
Ron Estrin;C. Greif
我们介绍了一个新的家庭的鞍点最小残差方法迭代求解鞍点系统使用最小或准最小残差的方法。没有对称性假设。该方法的基本机制是一种新的同时双对角化过程，产生一个简化的鞍点矩阵的投影Krylov样子空间，并允许一个单调的短递归迭代计划。我们开发了一些变体，展示了我们的方法的优点，推导出最优性条件，并讨论了与现有方法的连接。数值实验说明了这种新的家庭的方法的优点。
We introduce a new family of saddle-point minimum residual methods for iteratively solving saddle-point systems using a minimum or quasi-minimum residual approach. No symmetry assumptions are made. The basic mechanism underlying the method is a novel simultaneous bidiagonalization procedure that yields a simplified saddle-point matrix on a projected Krylov-like subspace and allows for a monotonic short-recurrence iterative scheme. We develop a few variants, demonstrate the advantages of our approach, derive optimality conditions, and discuss connections to existing methods. Numerical experiments illustrate the merits of this new family of methods.