On Solving the Large Sparse Generalized Eigenvalue Problem
Wisniewski, John Aruthur
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https://hdl.handle.net/2142/66452
Description
Title
On Solving the Large Sparse Generalized Eigenvalue Problem
Author(s)
Wisniewski, John Aruthur
Issue Date
1981
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
This thesis presents an algorithm for solving the large sparse generalized eigenvalue problem Ax = (lamda)Bx. The matrices A and B are assumed to be symmetric, and haphazardly sparse, with B being positive definite. The problem is treated from a constrained optimization approach and an inverse iteration is developed which requires the solution of linear algebraic systems only to the accuracy demanded by a given subspace. The convergence of the method is discussed, and the rate of convergence is improved by using shifting with the Ritz approximations. Numerical results are presented, and aspects concerning an implementation on a parallel computer are discussed.
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