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- I Gohberg, V Olshevsky, Comp
- 1994

Fast algorithms for computing the product by a vector are presented for a number of classes of matrices whose properties relate to the properties of Toeplitz, Vandermonde or Cauchy matrices (these matrices are deened using the concept of displacement of a matrix) and also for their inverses. All the actions which are not dependent upon the coordinates of… (More)

- I. GOHBERG, V. OLSHEVSKY
- 2010

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)

- Israel Gohberg, Vadim Olshevsky
- J. Complexity
- 1994

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)

- Vadim Olshevsky, Amin Shokrollahi
- STOC
- 2000

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)

- Vadim Olshevsky, Amin Shokrollahi
- STOC
- 1999

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)

Algebraic coding theory is one of the areas that routinely gives rise to computational problems involving various structured matrices, such as Hankel, Vandermonde, Cauchy matrices, and certain generalizations thereof. Their structure has often been used to derive efficient algorithms; however, the use of the structure was pattern-specific, without applying… (More)

- I Gohberg, T Kailath, V Olshevsky, Ag, F R ? R A
- 1995

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)

- I Gohberg, V Olshevsky
- 1994

This paper contains two fast algorithms for inversion of Chebyshev{Vander-monde matrices of the rst and second kind. They are based on special representations of the Bezoutians of Chebyshev polynomials of both kinds. The paper also contains the results of numerical experiments which show that the algorithms proposed here are not only much faster, but also… (More)

- Thomas Kailath, Vadim Olshevsky
- SIAM J. Matrix Analysis Applications
- 2005

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)