A fast solver for linear systems with displacement structure

We describe a fast solver for linear systems with reconstructible Cauchylike structure, which requires O(rn2 ) 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.

• Type: Journal
• Year: 2010
• Where: NA
• Authors: Antonio Arico, Giuseppe Rodriguez
• Keywords: Generalized Schur Algorithm, Linear Systems, NA 2010, Suitable Augmented Matrix