Lattice Algorithms for Computing QR and Cholesky Factors in the Least Squares Theory of Linear Prediction

Abstract

This paper poses a sequence of linear prediction problems that are a little different from those previously posed. By solving the sequence of problems we are able to QR factor data matrices of the type usually associated with correlation, pre and post-windowed, and covariance methods of linear prediction. Our solutions cover the forward, backward, and forward-backward problems. The QR factor orthogonalizes the data matrix and solves the problem of Cholesky factoring the experimental correlation matrix and its inverse. This means we may use generalize Levinson algorithms to derive generalized QR algorithms, which are then used to derive generalized Schur algorithms. All three algorithms are true lattice algorithms that may be implemented either on a vector machine or on a multi-tier lattice, and all three algorithms generate generalized reflection coefficients that may be used for filtering or classification. Keywords: Toeplitz matrices; Factorization; Covariance; Matrix theory.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1987
Accession Number
ADA196454

Entities

People

  • Cedric J. Demeure
  • Louis L. Scharf

Organizations

  • University of Colorado Boulder

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Coefficients
  • Colorado
  • Computations
  • Covariance
  • Data Science
  • Equations
  • Filtration
  • Information Science
  • Linear Algebra
  • Mathematics
  • Military Research
  • Reflection
  • Security
  • Sequences
  • Universities

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra