Balancing the Generalized Eigenvalue Problem
Copyright policy )Balancing the Generalized Eigenvalue Problem
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.
Numerical computation of eigenvalues and eigenvectors of matrices, diagonal transformation, generalized eigenvalue, Numerical computation of matrix norms, conditioning, scaling, scaling, balancing, QZ algorithm, graded matrix
Numerical computation of eigenvalues and eigenvectors of matrices, diagonal transformation, generalized eigenvalue, Numerical computation of matrix norms, conditioning, scaling, scaling, balancing, QZ algorithm, graded matrix
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