An inverse factorization algorithm for linear prediction
type: Item
instance of: scholarly article
title: An inverse factorization algorithm for linear prediction
zbMATH Open document ID: 0763.65108
DOI: 10.1016/0024-3795(92)90025-6
published in: Linear Algebra and its Applications
publication date: 1992-09-27T00:00:00Z
review text: A method which is based on a fast \(QR\) factorization algorithm of \textit{A. W. Bojanczyk}, \textit{R. P. Brent} and \textit{F. R. de Hoog} [Numer. Math. 49, 81-94 (1986; Zbl 0574.65019)] is described. An inverse factorization technique is presented for solving linear prediction problems arising in signal processing. The algorithm uses the rectangular Toeplitz structure of the data to recursively compute the prediction error and to solve the problem when the optimum filter order is found. The novelty of the scheme is the use of an inverse factorization scheme due to \textit{C.-T. Pan} and the second author [J. Comput. Appl. Math. 27, No. 1/2, 109-127 (1989; Zbl 0677.65037)] for solving the linear prediction problem with low computational complexity and without the need for solving triangular systems. A systolic array implementation of these problems is realized. It is shown that this algorithm has low numerical complexity, and can be implemented on a linear systolic array in \(n+(1/2)p_ 0^ 2+(13/2)p_ 0\) time steps, where \(n\) is the number of data samples and \(p_ 0\) is the optimal order of the predictor.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 60G25
zbMATH DE Number: 64487
zbMATH Keywords: fast \(QR\) factorization algorithm
zbMATH Keywords: linear prediction
zbMATH Keywords: signal processing
zbMATH Keywords: optimum filter order
zbMATH Keywords: inverse factorization scheme
zbMATH Keywords: computational complexity
zbMATH Keywords: systolic array
author: James G. Nagy
author: Robert J. Plemmons
reviewed by: I. Dimov
MaRDI profile type: Publication
full work available at URL: 0024-3795(92)90025-6
OpenAlex ID: W2068747293
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Wikidata QID: Q127014866
description: scientific article; zbMATH DE number 64487