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na31

swMATH ID: 11500
Software Authors: Aricò, Antonio; Rodriguez, Giuseppe
Description: A fast solver for linear systems with displacement structure. 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. (netlib numeralgo na31)
Homepage: http://www.netlib.org/numeralgo/index.html
Dependencies: Matlab
Keywords: displacement structure; Toeplitz(+Hankel)-like matrix; generalized Schur algorithm; augmented matrix; matlab toolbox; Cauchy-like matrix; Vandermonde-like linear systems; numerical experiments
Related Software: drsolve; mctoolbox; tpls; toms729gw; smt; TOEPLITZ; Matlab; MATLAB expm; mftoolbox; JDQZ; JDQR; hlib; testmatrix; UTV; RestoreTools; Netlib; FFTW; SLICOT; Regularization tools; BLAS
Cited in: 9 Publications

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