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Solving Toeplitz systems after extension and transformation

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Abstract

Subject of the paper are systems of linear equations with an indefinite or nonsymmetric Toeplitz coefficient matrixT=[a i−j ]. In order to avoid instabilities which often occur during the application of Levinson and Schur type algorithms for these matrices transformation techniques combined with pivoting strategies have been proposed in earlier papers, starting with [19]. These transformations have some deficiencies. To overcome these we propose to carry out the transformation after a convenient extension. In particular, we discuss the transformation after extension into paired Vandermonde matrices. The corresponding systems admitO(n 2) complexity complete pivoting.

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  1. Dept. of Math. & Comp. Sci., Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait

    Georg Heinig

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  1. Georg Heinig
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Heinig, G. Solving Toeplitz systems after extension and transformation. Calcolo 33, 115–129 (1996). https://doi.org/10.1007/BF02575712

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