THE FAST ALGORITHM FOR SIMULTANEOUS ORTHOGONAL REDUCTION OF MATRICES TO THE TRIANGULAR FORM

Abstract. We consider a problem of simultaneous reduction of a sequence of matrices by means of orthogonal transformations. We show that such reduction can be performed by a series of the deflation steps. At each deflation step a simultaneous eigenvalue problem, which is a direct generalization of the generalized eigenvalue problem, is solved. A fast variant of Gauss-Newton algorithm for its solution was proposed and the local convergence properties were investigated. We illustrate the effectiveness of our algorithm by some numerical examples. Key words. Simultaneous reduction of matrices, fast algorithms, convergence estimates 1. Introduction. Th