MA21
PACKAGE SPECIFICATION HSL ARCHIVE
Warning: Subroutine
MA21
performs functions which are adequately treated by routines in other
standard subroutine libraries (for example,
LAPACK
). The use of this routine is not recommended, and
it may be removed from future releases of this library.
1 SUMMARY
Given an n by n matrix A ={a } performs one or more of the following tasks.
ij n×n
(a) solves the system of linear algebraic equations
n
a x =b i=1,2,...,n
∑
ij j i
j=1
given the right-hand sides b , i=1,2,...,n, and provides a re-entry facility for the rapid solution of further systems of
i
equations which have the same elements a .
ij
−1
(b) computes the inverse matrix A of A.
(c) computes the value of the determinant of A.
The subroutine will optionally perform iterative refinement in order to both improve the accuracy of the answer
(solution or inverse) and provide error estimates based either on the precision of the computer or on user supplied
accuracy information. An option for scaling the matrix is provided.
The method is basically Gaussian elimination with partial pivoting, implicit scaling and iterative refinement and
applying small random perturbations in order to estimate errors, see S. Marlow and J.K. Reid, AERE R.6899.
ATTRIBUTES — Version: 1.0.0. Types:
MA21A
;
MA21AD
. Calls:
FA01
;
FD05
. Original date: August 1971. Origin:
S.Marlow and J.K.Reid, Harwell.
2 HOW TO USE THE PACKAGE
2.1 Entries and argument lists
The entry points
To solve systems of linear equations as in § 1(a).
The single precision version
CALL MA21A(A,IA,N,B,W,E)
The double precision version
CALL MA21AD(A,IA,N,B,W,E)
To find inverse of matrix A in § 1(b).
All use is subject to licence.
MA21
v 1.0.0
http://www.hsl.rl.ac.uk/ 1
Documentation date: 8th February 2011
