基于扩展FEAST的大规模特征值求解问题研究  

LARGE SCALE EIGENVALUE SOLUTION BASED ON EXTENDED FEAST

作　　者：李玲玲 李华 Li Lingling;Li Hua(School of Mathematical and Physical Science,Henan University of Urban Construction,Pingdingshan 467036,Henan,China)

机构地区：[1]河南城建学院数理学院,河南平顶山467036

出　　处：《计算机应用与软件》2021年第7期289-294,共6页Computer Applications and Software

基　　金：河南省高等学校重点科研项目(15A110012)。

摘　　要：为了求解非线性特征值问题,在线性FEAST特征值算法的基础上,提出一种非线性FEAST扩展算法。通过将复平面分割为不相交的区域集合,计算每个区域的特征对。扩展算法使用与线性FEAST算法相同的一系列运算,通过修改围道积分来支持非线性特征值求解的固定移位集合和固定子空间维数。与线性FEAST算法相似,扩展算法可以通过并行求解额外的线性系统,改进数值围道积分或提升近似特征向量子空间的维数,从而提高非线性FEAST的收敛速度。通过三个计算模型问题验证了非线性FEAST算法的多项式特征值行为。To solve the nonlinear eigenvalue problem,a nonlinear FEAST extended algorithm is proposed based on the linear FEAST eigenvalue algorithm.By dividing the complex plane into disjoint sets of regions,the feature pairs of each region were calculated.The extended algorithm used the same series of operations as the linear FEAST algorithm.By modifying the contour integral,it supports the fixed shift set and the fixed subspace dimension for solving the non-linear eigenvalues.Similar to the linear FEAST algorithm,the extended algorithm can improve the convergence speed of the nonlinear FEAST by solving additional linear systems in parallel,improving the numerical contour integral or increasing the dimension of the approximate eigenvector subspace.Three physical model problems verify the polynomial eigenvalue behavior of the nonlinear FEAST algorithm.

关 键 词：非线性特征值 线性FEAST 非线性FEAST 围道积分 收敛速度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]