Linear stationary second-degree methods for the solution of large linear systems Page: 4 of 24
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Linear Stationary Second-Degree Methods
for the Solution of Large Linear Systems *
David M. Young
David R. Kincaid
July 9, 1990
The optimum linear stationary second-degree iterative method for
solving linear systems of equations is not as good in general as the
optimum semi-iterative method. However, for a suitable choice of
parameters, the rate of convergence of the stationary method is very
nearly as good as that of the semi-iterative method. We present a
straighforward determination of these optimum parameter values and
the asymptotic rate of convergence.
In this paper, we consider a class of linear stationary second-degree methods
for solving the linear system
Au = b, (1)
where A is a given real nonsingular N x N matrix and b is a given vector or
N x 1 (column) matrix. The second-degree methods that we shall consider
are related to a basic linear stationary method of first degree of the form
(n+1) G(n) + k, Ofv Oki W (2)
*This work was supported, in part, by the National Science Foundation under Grant
ASC-8917592, by the Department of Energy under Grant DE-FG05-87ER25048, and by
Cray Research, Inc., under Grant LTR DTD with The University of Texas at Austin.
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Young, D.M. & Kincaid, D.R. Linear stationary second-degree methods for the solution of large linear systems, report, July 9, 1990; United States. (digital.library.unt.edu/ark:/67531/metadc710495/m1/4/: accessed November 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.