On the generalized ADI method for the matrix equation X -AXB = C

Authors:
J. P. Thiran;M. Matelart;B. Le Bailly
Affiliations:
Department of Mathematics, Facultés Univ. de Namur, Rempart de la Vierge 8, Namur B-5000, Belgium;Department of Mathematics, Facultés Univ. de Namur, Rempart de la Vierge 8. Namur B-5000, Belgium;Department of Mathematics, Facultés Univ. de Namur, Rempart de la Vierge 8. Namur B-5000, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 11
Cited 1

Topics in matrix analysis

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Weighted least squares solutions to general coupled Sylvester matrix equations

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Abstract

The paper investigates a rational approximation problem in connection with the convergence analysis of the ADI iterative method applied to the matrix equation X - AXB = C. In the real case, a complete theory on the characterization and unicity of the optimal solution as well as on the convergence of a Remes like algorithm for its computation, is presented. Numerical experiments provide some comparison with asymptotically optimal solutions which have been previously reported, particularly in applications for image restoration.