Fast Simultaneous Orthogonal Reduction to Triangular Matrices
Ivan Valer'evich Oseledets, Dmitry Savostyanov, E. E. Tyrtyshnikov · SIAM Journal on Matrix Analysis and Applications · 2009
A new algorithm is presented for simultaneous reduction of a given finite sequence of square matrices to upper triangular matrices by means of orthogonal transformations. The reduction is performed through a series of deflation steps, where each step contains a simultaneous eigenvalue problem being a direct generalization of the generalized eigenvalue problem. To solve the latter, a fast variant of the Gauss–Newton algorithm is proposed with some results on its local convergence properties (quadratic for the exact and linear for the approximate reduction) and numerical examples are provided.