Thursday, October 30

Fast and Superfast Toeplitz Solvers

10:00 AM-12:00 PM
Room: Ballroom 3

Toeplitz systems arise in a variety of applications in mathematics and engineering, including signal processing, adaptive filtering, circuit simulations, geodesy, partial differential equations, Pade approximations, minimal realizations, and many others. From the practical standpoint it is important to exploit the structure of these systems to design special efficient algorithms which compute the solution rapidly and without loss of numerical accuracy. There are two classical fast algorithms, the Levinson and the Schur algorithms which exploit the structure to solve a Toeplitz system in only O(n^2) arithmetic operations (general algorithms are slower, requiring O(n^3)). The purpose of this minisymposium is to report a recent progress in the design of superfast accurate methods which require even less, O(n log^2 n) operations. The presentations will cover both direct and iterative superfast methods, multigrid and splitting approaches; they will pay attention to both efficiency (speed, memory, amenability to parallel implementations) and numerical accuracy.

Organizer: Georg Heinig,
Kuwait University, Kuwait;
and Vadim Olshevsky,
Stanford University

10:00 Superfast Algorithms for Positive Definite Toeplitz Systems
Gregory S. Ammar, Northern Illinois University
10:30 Practical Multigrid Methods for Toeplitz Matrices
Thomas K. Huckle, Institut fuer Informatik, TU Muenchen, Germany
11:00 Displacement Structure Approach to Discrete Transform Based Preconditioners of G. Strang and T. Chan Types
Vadim Olshevsky, Organizer
11:30 The Splitting Approach for Real Based Superfast Toeplitz Solvers
Georg Heinig, Organizer and Marc Van Barel, Leuven, Belgium

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MMD, 6/5/97
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MMD, 10/24/97