PARALLEL HOMOTOPY ALGORITHM FOR SYMMETRICAL LARGE SPARSE EIGENPROBLEMS

作     者：HUANG, LJ LI, TY 

作者机构：ROCKFORD COLLDEPT MATHROCKFORDIL 61108 MICHIGAN STATE UNIVDEPT MATHE LANSINGMI 48824 

出 版 物：《JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS》 (J. Comput. Appl. Math.)

年 卷 期：1995年第60卷第1-2期

页      面：77-100页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation  NSF  (CCR-9024840) 

主　　题：EIGENPROBLEMS HOMOTOPY ALGORITHM PARALLELISM 

摘      要：In this paper, the homotopy continuation method is applied to solve the eigenproblem Ax = lambda x, lambda is an element of R, x is an element of R(n)\{0} or a symmetric large sparge matrix A. A one-parameter family of matrices A(t) = tA + (1 - t) D is introduced and the eigenproblem A(t)x(t) = lambda(t)x(t) is considered for t is an element of [0, 1]. We discuss the problem of choosing an optimal starting matrix A(0) = D and consider the regularity and bifurcation problem of lambda(t) and x(t). A homotopy continuation algorithm is constructed and implemented on both parallel and vector machines for several types of matrices. The numerical experiments show that our method is efficient and highly parallel.