AN EXTENSION OF THE QZ ALGORITHM FOR SOLVING THE GENERALIZED MATRIX EIGENVALUE PROBLEM

摘要

An algorithm called the combination shift QZ algorithm is presented for solving the generalized matrix eigenvalue problem. This new algorithm is an extension of Moler and Stewart's QZ algorithm with some added features for saving time and operations. Also, some additional properties of the QR algorithm which were not practical to implement in the QZ algorithm can be generalized with the combination shift QZ algorithm. Numerous test cases are presented to give practical application tests for the algorithm. Based on the results presented in this paper, this algorithm should be preferred over existing algorithms which attempt to solve the class of generalized eigenproblems where both matrices are singular or nearly singular.