BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-92-05
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Adaptive Chebyshev iterative methods for nonsymmetric linear
               systems based on modified moments
        TYPE:: Manuscript
      AUTHOR:: Calvetti, Daniela
      AUTHOR:: Golub, Gene H.
      AUTHOR:: Reichel, Lothar
        DATE:: May 1992
       PAGES:: 26
    ABSTRACT:: Large, sparse nonsymmetric systems of linear equations with a
               matrix whose eigenvalues lie in the right half plane may be
               solved by an iterative method based on Chebyshev polynomials
               for an interval in the complex plane. Knowledge of the convex
               hull of the spectrum of the matrix is required in order to
               choose parameters upon which the iteration depends. Adaptive
               Chebyshev algorithms, in which these parameters are
               determined by using eigenvalue estimates computed by the
               power method or modifications thereof, have been described by
               Manteuffel [1978]. This paper presents adaptive Chebyshev
               iterative methods, in which eigenvalue estimates are computed
               from modified moments determined during the iterations. The
               computation of eigenvalue estimates from modified moments
               requires less computer storage than when eigenvalue estimates
               are computed by a power method and yields faster convergence
               for many problems.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-92-05