An Algorithm for Generalized Matrix Eigenvalue Problems.

  title={An Algorithm for Generalized Matrix Eigenvalue Problems.},
  author={Cleve B. Moler and G. W. Stewart},
  journal={SIAM Journal on Numerical Analysis},
  • C. Moler, G. Stewart
  • Published 1 April 1973
  • Computer Science
  • SIAM Journal on Numerical Analysis
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. 
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