EFFICIENT PRECONDITIONING FOR SEQUENCES OF PARAMETRIC COMPLEX SYMMETRIC LINEAR SYSTEMS
EFFICIENT PRECONDITIONING FOR SEQUENCES OF PARAMETRIC COMPLEX SYMMETRIC LINEAR SYSTEMS
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发表时间：
2004
影响因子：
1.3
通讯作者：
D. Bertaccini
中科院分区：
文献类型：
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作者：
D. Bertaccini
形式为Ajxj = bj，j = 0;：; s，Aj = A + jEj，A Hermitian，E0;：; Es复对角矩阵和0;：; s标量复参数的复对称线性系统的序列的解出现在各种具有挑战性的问题中。这是与时间相关的偏微分方程的情况下，在量子色动力学格规范计算，亥姆霍兹方程，移位和反演和雅可比戴维森算法的大规模本征值计算，控制理论和许多其他问题。如果A是对称的并且有真实的元素，那么Aj是复对称的。本文考虑了A为Hermitian正半无限元，Re（j）为0且使得Ej，j = 0;：; s的对角元具有非负真实的部分的情形.介绍并分析了基于矩阵A和A1的不完全分解的更新策略。数值解序列的代数线性系统的离散化的真实的和复杂的Helmholtz方程和差分方程在一个矩形说明所提出的方法的性能。
Solution of sequences of complex symmetric linear systems of the form Ajxj = bj, j = 0; :::; s, Aj = A + jEj, A Hermitian, E0; :::; Es complex diagonal matrices and 0; :::; s scalar complex parameters arise in a variety of challenging problems. This is the case of time dependent PDEs; lattice gauge computations in quantum chromodynamics; the Helmholtz equation; shift-and- invert and Jacobi{Davidson algorithms for large-scale eigenvalue calculations; problems in control theory and many others. If A is symmetric and has real entries then Aj is complex symmetric. The case A Hermitian positive semidenite, Re( j) 0 and such that the diagonal entries of Ej, j = 0; :::; s have nonnegative real part is considered here. Some strategies based on the update of incomplete factorizations of the matrix A and A 1 are introduced and analyzed. The numerical solution of sequences of algebraic linear systems from the discretization of the real and complex Helmholtz equation and of the diusion equation in a rectangle illustrate the performance of the proposed approaches.