Vadim Olshevsky

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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)
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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)
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)
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)
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)