Some Remarks on the Generalised Bareiss and Levinson Algorithms

Abstract

The Bareiss (or Schur) and Levinson algorithms are the most popular algorithms for solving linear systems with dense n x n Toeplitz coefficient matrix in O(n squared) arithmetic operations. Both algorithms have been generalised to solve linear systems whose n x n coefficient matrices A are not necessarily Toeplitz (in O(n cubed) operations). We show in this paper that the generalised Levinson algorithm is a direct consequence of the generalised Bareiss algorithm, thereby considerably simplifying its presentation in comparison to previous work.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1990
Accession Number
ADA221957

Entities

People

  • Ilse Ipsen

Organizations

  • Yale University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Coefficients
  • Computations
  • Computer Science
  • Contrast
  • Elimination
  • Equations
  • Error Analysis
  • Integral Equations
  • Linear Systems
  • Matrix Theory
  • Numbers
  • Real Numbers
  • Rotation
  • Time Series Analysis
  • Two Dimensional

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.