<DOC>
<DOCNO>
1088
</DOCNO>
<TITLE>
iterative methods for solving partial difference equations of elliptic
type .
</TITLE>
<AUTHOR>
young, d.
</AUTHOR>
<BIBLIO>
trans. amer. math. soc. vol. 76, p. 92, 1954 .
</BIBLIO>
<TEXT>
this paper considers linear systems /1/ where a includes matrices of a
sort frequently occurring in the solution of elliptic partial differential
equations by difference methods /in particular, a o/ . rewriting
 superscript is number of iteration cycle/ are used to compute u
when u are used . also, one may /over-relax/ ..
ser. a. 210, 307-357 /1910/ who suggested changing from time to time
to speed up convergence . in the present paper over-relaxation /with
fixed w/ is combined with immediate introduction of newly-computed u's,
a la gauss-seidel . various theorems on convergence are proved$. in
particular, it is shown that there exists an ordering of the equations
and an optimum value wb such that in general /3/ converges much more
rapidly than the gauss-seidel method /w 1/ . means are suggested for
estimating wb,. the sensitivity of the rate of convergence to the choice
 of w is studied . the paper concludes with a theoretical comparison of
gauss-seidel and the method proposed, /successive over-relaxation/, for
solving dirichlet's difference problem over a square using a high-speed
computing machine .
</TEXT>
</DOC>
