The Fast Algorithm for Simultaneous Orthogonal Reduction of Matrices to the Triangular Form
نویسنده
چکیده
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.
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