Matrix Downdating Techniques For Signal Processing

Adam W. Bojanczyk; Allan O. Steinhardt

doi:10.1117/12.948492

23 February 1988 Matrix Downdating Techniques For Signal Processing

Adam W. Bojanczyk, Allan O. Steinhardt

Proceedings Volume 0975, Advanced Algorithms and Architectures for Signal Processing III; (1988) https://doi.org/10.1117/12.948492
Event: 32nd Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1988, San Diego, CA, United States

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

Citation Download Citation

Adam W. Bojanczyk and Allan O. Steinhardt "Matrix Downdating Techniques For Signal Processing", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); https://doi.org/10.1117/12.948492

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