Fast Simultaneous Orthogonal Reduction to Triangular Matrices

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.

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