A fast solver for linear systems with displacement structure

A fast solver for linear systems with displacement structure

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Article ID: iaor20108164
Volume: 55
Issue: 4
Start Page Number: 529
End Page Number: 556
Publication Date: Dec 2010
Journal: Numerical Algorithms
Authors: ,
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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