1 November 1990 Adaptive Lanczos methods for recursive condition estimation
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Abstract
Estimates for the condition number of a matrix are useful in many areas of scientific computing including: recursive least squares computations optimization eigenanalysis and general nonlinear problems solved by linearization techniques where matrix modification techniques are used. The purpose of this paper is to propose an adaptive Lanczos estimator scheme which we call ale for tracking the condition number of the modified matrix over time. Applications to recursive least squares (RLS) computations using the covariance method with sliding data windows are considered. ale is fast for relatively small n - parameter problems arising in RLS methods in control and signal processing and is adaptive over time i. e. estimates at time t are used to produce estimates at time t + 1 . Comparisons are made with other adaptive and non-adaptive condition estimators for recursive least squares problems. Numerical experiments are reported indicating that ale yields a very accurate recursive condition estimator.
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William R. Ferng, William R. Ferng, Gene H. Golub, Gene H. Golub, Robert J. Plemmons, Robert J. Plemmons, "Adaptive Lanczos methods for recursive condition estimation", Proc. SPIE 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations, (1 November 1990); doi: 10.1117/12.23489; https://doi.org/10.1117/12.23489
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