a node ordering algorithm to speed up the solution of ...

A NODE ORDERING ALGORITHM TO SPEED UP THE SOLUTION OF SPARSE MATRIX AND SPARSE VECTOR LINEAR EQUATION SYSTEMS Antonio G6mez and Leopoldo G. Franquelo Depto. de Ingen. Electrica, Electr6nica y Automatica Universidad de Sevilla, Spain

ABSTRACT. Recently, mothoda

in

mor e

ord . ~

to

a tt e ntion

hag b e en

r e duc e the

d o voted

comput a tion a l

to

spar g e

burden when

vector aolvin~

sparae systems o! linear equatio n s. Theae methode exploit the sparsity of the independent vector

and/or the deaire to know

only a subset of

tho unknown vector. They a re al a o a pplic a ble when ret a ctorization o f s ll a htly modifi e d ma trix i .

This paper propOS8a a scheme to of

reducing the

number

•

r . quir e d . order the nodes with the purpoae

of operations

when

applying sparaB

vector

methoda.

INT RODUCTION. Sparae matrix equatlonu of the form:

Ax • b a ppear 1n performs

ma ny

(1)

e n~ine e rin~

fi e ld s .

a ap a rsity- orianted

LOU

Tho s tandard decomposition

o olution procod u r e of

A.

followed

by

!o r ward a nd b a ck operationa On tho independent vector, b. Thl . a)

Pa p e r d .a l .

Repe a ted

with two kind .

solution at

(1)

when

of problemsl mat r ix

A 1s

slightly

modi!ied

(parti a l ma t r ix r . t a ctori:etion problem) Ill. b) Solution

ot

(1) when

elements or a small needod

(8p a r ~ e

either VQctor

b

ha D only

number or elements in the

vector problem) [2l.

a

t ew non - zero

unknown vector x i8

lIS

compeno~llon

the~e

~elhod ••

•• pecla are 8l.on~ly ralatad to r •• l control ot .tacl.leal powar .yat.ma.

op.r~tlon

A recant paper v~ctor

apar ••

r.4u~tlon lh~l

be

1n

1n

~ulhor.

.y.t.~

power CQun~

oparatlona lh.

paper,

develop~d

.1. (2) emph •• ized

by Tinney.t

~.thod.

co~p.r.d

the intareat or

.hQwln~

to convenllonal

a dramatic Method., In

naw nod. orderlnl alcorlthma had to

lh~l

noled

1n order to

analyala,

aparalty ot L- 1

enhanca the