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A fast solver for linear systems with displacement structure

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Abstract

We describe a fast solver for linear systems with reconstructible Cauchy-like structure, which requires O(rn 2) floating point operations and O(rn) memory locations, where n is the size of the matrix and r its displacement rank. The solver is based on the application of the generalized Schur algorithm to a suitable augmented matrix, under some assumptions on the knots of the Cauchy-like matrix. It includes various pivoting strategies, already discussed in the literature, and a new algorithm, which only requires reconstructibility. We have developed a software package, written in Matlab and C-MEX, which provides a robust implementation of the above method. Our package also includes solvers for Toeplitz(+Hankel)-like and Vandermonde-like linear systems, as these structures can be reduced to Cauchy-like by fast and stable transforms. Numerical experiments demonstrate the effectiveness of the software.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123, Cagliari, Italy

    Antonio Aricò & Giuseppe Rodriguez

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  1. Antonio Aricò
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  2. Giuseppe Rodriguez
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Correspondence to Giuseppe Rodriguez.

Additional information

This work was partially supported by MIUR, under the PRIN grant no. 20083KLJEZ-003, and by INdAM-GNCS.

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Aricò, A., Rodriguez, G. A fast solver for linear systems with displacement structure. Numer Algor 55, 529–556 (2010). https://doi.org/10.1007/s11075-010-9421-x

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