Title: Euclid, Padé and Lanczos, another golden braid
Authors: Bultheel, Adhemar ×
Van Barel, Marc
Issue Date: Apr-1993
Publisher: Department of Computer Science, K.U.Leuven
Series Title: TW Reports vol:TW188
Abstract: We describe how the Euclidean algorithm can be interpreted as a method to solve Pade approximation problems in a table with singular blocks and minimal partial realization problems of linear system theory. Its recursive structure also relates it to continued fraction expansions of formal series and generalizations of three term recurrence relations of formal (block) orthogonal polynomials. Hence, it can also be considered as a fast Gram-Schmidt procedure for orthogonalization with respect to an indefinite Gram matrix with Hankel structure and a fast Hankel factorizer in triangular factors. Finally, the link with the Lanczos algorithm for nonsymmetric matrices is made.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author

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