BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-90-07
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Adaptive Lanczos methods for recursive condition estimation
        TYPE:: Manuscript
      AUTHOR:: Ferng, William R.
      AUTHOR:: Golub, Gene H.
      AUTHOR:: Plemmons, Robert J.
        DATE:: June 1990
       PAGES:: 22
    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.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-90-07