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Fast On 2 implementation of Gaussian elimination with partial pivoting is designed for matrices possessing Cauchy-like displacement structure. We show how Toeplitzz like, Toeplitz-plus-Hankelllike and Vandermonde-like matrices can be transformed into Cauchyylike matrices by using Discrete Fourier, Cosine or Sine Transform matrices. In particular this allows(More)
In this paper the problem of complexity of multiplication of a matrix with a vector is studied for Toeplitz, Hankel, Vandermonde and Cauchy matrices and for matrices connected with them (i.e. for transpose, inverse and transpose to inverse matrices). The proposed algorithms have complexities at most O(n log 2 n) ops and in a number of cases improve the(More)
Many important problems in pure and applied mathematics and engineering can be reduced to linear algebra on dense structured matrices. The structure of these dense matrices is understood in the sense that their n z entries can be "compressed" to a smaller number O(n) of parameters. Operating directly on these paxameters allows one to design efficient fast(More)
Using methods originating in numerical analysis, we will develop a unified framework for derivation of efficient list decoding algorithms for algebraic-geometric codes. We will demonstrate our method by accelerating Sudan's list decoding algorithm for Reed-Solomon codes [22], its generalization to algebraic-geometric codes by Shokrollahi and Wasserman [21],(More)
Fast O(n 2) implementation of Gaussian elimination with partial pivoting is designed for matrices possessing Cauchy-like displacement structure. We show how Toeplitz{ like, Toeplitz-plus-Hankel{like and Vandermonde-like matrices can be transformed into Cauchy{like matrices by using Discrete Fourier, Cosine or Sine Transform matrices. In particular this(More)
The QR iteration method for tridiagonal matrices is in the heart of one classical method to solve the general eigenvalue problem. In this paper we consider the more general class of quasiseparable matrices that includes not only tridiagonal but also companion, comrade, unitary Hessenberg and semiseparble matrices. A fast QR iteration method exploiting the(More)
In this paper a displacement structure technique is used to design a class of new precondition-ers for the conjugate gradient method applied to the solution of large Toeplitz linear equations. Explicit formulas are suggested for the G.Strang-type and for the T.Chan-type precondition-ers belonging to any of 8 classes of matrices diagonalized by the(More)