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 Cauchylike 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 Cauchylike 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 CMEX, which provides a robust implementation of the above method. Our package also includes solvers for Toeplitz(+Hankel)like and Vandermondelike linear systems, as these structures can be reduced to Cauchylike 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; Cauchylike matrix; Vandermondelike linear systems; numerical experiments 
Related Software:  drsolve; tpls; mctoolbox; toms729gw; smt; TOEPLITZ; Matlab; MATLAB expm; mftoolbox; JDQZ; JDQR; hlib; testmatrix; UTV; RestoreTools; Netlib; FFTW; SLICOT; Regularization tools; BLAS 
Cited in:  11 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

A fast solver for linear systems with displacement structure. Zbl 1203.65062 Aricò, Antonio; Rodriguez, Giuseppe 
2010

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Cited by 18 Authors
Cited in 5 Serials
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