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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 de ned 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)

In this paper we use a discrete transmission line model (known to geophysicists as a layered earth model) to derive several computationally eÆcient solutions for the following three problems. (i) As is well-known, a Hessenberg matrix capturing recurrence relations for Szeg}o polynomials di ers from unitary only by its last column. Hence, the rst problem is… (More)

- Vadim Olshevsky, Amin Shokrollahi
- STOC
- 2000

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed fbr prot]t or commercial advantage and that copies bear this notice and the lull citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to… (More)

- I. GOHBERG, V. OLSHEVSKY
- 2010

Fast 0(n2) 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 Vandermondelike matrices can be transformed into Cauchy-like matrices by using Discrete Fourier, Cosine or Sine Transform matrices. In particular this allows… (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, 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)

- T Kailath, V Olshevsky
- 1995

In this paper we use the displacement structure concept to introduce a new class of matrices, designated as Chebyshev{Vandermonde{like matrices, generalizing ordinary Chebyshev{ Vandermonde matrices, studied earlier by diierent authors. Among other results the displacement structure approach allows us to give a nice explanation for the form of the… (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 algebraicgeometric 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)

- 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 preconditioners 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 preconditioners belonging to any of 8 classes of matrices diagonalized by the… (More)

Using methods originating in numerical analysis, we will develop a uni ed framework for derivation of eÆcient algorithms for decoding several classes of algebraic 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… (More)