Stationary discrete-time covariance factorization using Newton-Raphson iteration

Langford B. White; Brian D.O. Anderson

doi:10.1007/BF01211561

Stationary discrete-time covariance factorization using Newton-Raphson iteration

Langford B. White^*, Brian D.O. Anderson

^*Corresponding author for this work

School of Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in l₁ provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is suggested.

Original language	English
Pages (from-to)	263-279
Number of pages	17
Journal	Mathematics of Control, Signals, and Systems
Volume	5
Issue number	3
DOIs	https://doi.org/10.1007/BF01211561
Publication status	Published - Sept 1992

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10.1007/BF01211561

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title = "Stationary discrete-time covariance factorization using Newton-Raphson iteration",

abstract = "The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in l1 provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is suggested.",

keywords = "Covariance factorization, Error localization, Newton-Raphson, Spectral factorization, Wiener-Hopf equations",

author = "White, \{Langford B.\} and Anderson, \{Brian D.O.\}",

year = "1992",

month = sep,

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AU - White, Langford B.

AU - Anderson, Brian D.O.

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N2 - The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in l1 provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is suggested.

AB - The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in l1 provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is suggested.

KW - Covariance factorization

KW - Error localization

KW - Newton-Raphson

KW - Spectral factorization

KW - Wiener-Hopf equations

UR - https://www.scopus.com/pages/publications/0026745318

U2 - 10.1007/BF01211561

DO - 10.1007/BF01211561

M3 - Article

AN - SCOPUS:0026745318

SN - 0932-4194

VL - 5

SP - 263

EP - 279

JO - Mathematics of Control, Signals, and Systems

JF - Mathematics of Control, Signals, and Systems

IS - 3

ER -

Stationary discrete-time covariance factorization using Newton-Raphson iteration

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