Solving symmetric-definite quadratic lambda-matrix problems without factorization

Journal Article · Sun Feb 28 19:00:00 EST 1982 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0903005· OSTI ID:6506875

Scott, D S ^[1]; Ward, R C

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1. Univ. of Texas, Austin

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda/sup 2/ C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented.

• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 6506875
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 3:1; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EIGENVALUES
EIGENVECTORS
EQUATIONS
EQUATIONS OF MOTION
GYROSCOPES
HERMITIAN MATRIX
MATHEMATICAL LOGIC
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
RITZ METHOD