BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-92-21
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: On the error computation for polynomial based iteration
               methods
        TYPE:: Manuscript
      AUTHOR:: Fischer, Bernd
      AUTHOR:: Golub, Gene H.
        DATE:: December 1992
       PAGES:: 12
    ABSTRACT:: In this note we investigate the Chebyshev iteration and the
               conjugate gradient method applied to the system of linear
               equations $Ax = f$ where $A$ is a symmetric, positive
               definite matrix. For both methods we present algorithms which
               approximate during the iteration process the $kth$ error
               $\varepsilon_k = \l x - x_k\l A$. The algorithms are based on
               the theory of modified moments and Gaussian quadrature. The
               proposed schemes are also applicable for other polynomial
               iteration schemes. Several examples, illustrating the
               performance of the described methods, are presented.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-92-21