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Proceedings Paper

Matrix Downdating Techniques For Signal Processing
Author(s): Adam W. Bojanczyk; Allan O. Steinhardt
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Paper Abstract

We are concerned with a problem of finding the triangular (Banachiewicz-Cholesky) factor of the covariance matrix after deleting observations from the corresponding linear least squares equations. Such a problem, often referred to as downdating, arises in classical signal processing as well as in various other broad ares of computing. Examples include recursive least squares estimation and filtering with a sliding rectangular window in adaptive signal processing, outlier suppression and robust regression in statistics, and the modification of Hessian matrices in the numerical solution of non-linear equations. Formally the problem can be described as follows: Given an n xn upper triangular matrix L and an n-dimensional vector x such that LTL - xxT > 0 find an n xn lower triangular matrix L such that LLT = LLT - XXT We will look at the following issues relevant to the downdating problem: - stability - rank-1 downdating algorithms - generalization to modifications of a higher rank

Paper Details

Date Published: 23 February 1988
PDF: 10 pages
Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); doi: 10.1117/12.948492
Show Author Affiliations
Adam W. Bojanczyk, Cornell University (United States)
Allan O. Steinhardt, Cornell University (United States)

Published in SPIE Proceedings Vol. 0975:
Advanced Algorithms and Architectures for Signal Processing III
Franklin T. Luk, Editor(s)

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