Balancing the Generalized Eigenvalue Problem
Robert C. Ward · SIAM Journal on Scientific and Statistical Computing · 1981
An algorithm is presented for balancing the A and B matrices prior to computing the eigensystem of the generalized eigenvalue problem $Ax = \lambda Bx$. The three-step algorithm is specifically designed to precede the $QZ$-type algorithms, but improved performance is expected from most eigensystem solvers. Permutations and two-sided diagonal transformations are applied to A and B to produce matrices with certain desirable properties. Test cases are presented to illustrate the improved accuracy of the computed eigenvalues.