An Algorithm for Generalized Matrix Eigenvalue Problems
- 1 April 1973
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 10 (2), 241-256
- https://doi.org/10.1137/0710024
Abstract
A new method, called the $QZ$ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B. Particular attention is paid to the degeneracies which result when B is singular. No inversions of B or its submatrices are used. The algorithm is a generalization of the $QR$ algorithm, and reduces to it when $B = I$. Problems involving higher powers of $\lambda $ are also mentioned.
Keywords
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