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IMA Journal of Applied Mathematics 1978 22(4):401-410; doi:10.1093/imamat/22.4.401
© 1978 by Institute of Mathematics and its Applications
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Solution of Linear Generalized Eigenvalue Problems Containing Singular Matrices

A. JENNINGS, J. HALLIDAY and M. J. COLE

Department of Civil Engineering, Queen's University Belfast, Northern Ireland
British Aerospace, Warton Aerodrome Nr. Preston, England

A general method is presented for the solution of the linear generalized eigenvalue problem Ax = {lambda}Bx, where matrices A and B may both be singular but ||A — {lambda}B|| 0. The procedure can easily be implemented on a digital computer using a Gaussian elimination algorithm with pivoting together with a QR eigensolution package. Results are given for two problems with sensitive eigenvalues.


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