Accession Number : ADA206867

Title :   Use of an Indefinite Inner Product for Computing Damped Natural Modes,

Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS

Personal Author(s) : Chen, H C ; Parlett, B N

PDF Url : ADA206867

Report Date : Nov 1988

Pagination or Media Count : 37

Abstract : A quadratic eigenvalue problem with symmetric positive definite coefficient matrics may be reduced to linear form while retaining symmetry in the new coefficients but neither of them will be positive definite. Formally the symmetric Lanczos algorithm and subspace iteration may be used to computer some eigenpairs of the linear problem. The trouble is that the basis vectors are orthogonal with respect to an indefinite inner product so there is no assurance that will be linearly independent. Nevertheless this is an attractive way to solve the original problem and we discuss how to implement it and how it relates to the unsymmetric Lanczos procedures. We discuss complex origin shifts, reothogonalization, and error bounds. Several methods for solving the reduced problem are mentioned but we have no fully satisfying technique. Some dangers are described and examples are given comparing our Lanczos program with a modified subspace iteration. (kr)

Descriptors :   *EIGENVALUES, *MATRIX THEORY, ALGORITHMS, COEFFICIENTS, DAMPING, LINEARITY, QUADRATIC EQUATIONS, REDUCTION

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE