GMRES - A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR-SYSTEMS
GMRES - A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR-SYSTEMS
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DOI：
10.1137/0907058
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发表时间：
1986-07-01
期刊：
影响因子：
--
通讯作者：
SCHULTZ, MH
中科院分区：
文献类型：
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作者：
SAAD, Y;SCHULTZ, MH
给出了求解线性方程组的一种迭代方法，它具有使Krylov子空间上的残差向量的范数在每一步最小的性质。该算法是由构造Krylov子空间的正交基的Arnoldi过程得到的。它可以被认为是Paige和Saunders的MinRes算法的推广，在理论上等价于广义共轭残差法(GCR)和ORTHODIR。与GCR和ORTHODIR相比，新算法有几个优点。
We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an-orthogonal basis of Krylov subspaces. It can be considered as a generalization of Paige and Saunders’ MINRES algorithm and is theoretically equivalent to the Generalized Conjugate Residual (GCR) method and to ORTHODIR. The new algorithm presents several advantages over GCR and ORTHODIR.