Premium
An efficient method for solving the eigenvalue problem for matrices having a skew‐symmetric (or skew‐Hermitian) component of low rank
Author(s) -
Garvey S. D.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620362404
Subject(s) - eigenvalues and eigenvectors , rank (graph theory) , hermitian matrix , mathematics , skew symmetric matrix , component (thermodynamics) , skew , matrix (chemical analysis) , dimension (graph theory) , symmetric matrix , mathematical analysis , combinatorics , pure mathematics , square matrix , physics , materials science , quantum mechanics , composite material , thermodynamics , astronomy
In the numerical modelling of mechanical systems, eigenvalue problems occur in connection with the evaluation of resonance frequencies, buckling modes and other more esoteric calculations. The matrices whose eigenvalues are sought sometimes have a skew‐symmetric component and the presence of this component adds significantly to the computational effort required. In many cases where there is a skew‐symmetric component, this component has a much lower rank than the symmetric component which generally has rank equal to its dimension. Examples of such cases abound in the area of rotor dynamics where the stiffness and damping matrices associated with journal bearings have significant skew‐symmetric components. The solution of the eigenvalue problem for an unsymmetric matrix takes more than twice the number of operations required for the solution of the eigenvalue problem for a symmetric matrix of the same dimension. This paper puts forward a new method for the solution of the eigenvalue problem for matrices having a skew‐symmetric component of low rank and shows that it is faster than established methods of comparable accuracy for the general unsymmetric NxN matrix if the rank of the skew‐symmetric component is less than N /7.3.