SHELS(3)

SYNOPSIS
SUBROUTINE SHELS (A, LDA, N, Q, B)

NAME
shels - Internal routine for SGMRES.

LIBRARY
SLATEC (SLAP)

CATEGORY
D2A4, D2B4

TYPE
SINGLE PRECISION (SHELS-S, DHELS-D)

KEYWORDS
GENERALIZED MINIMUM RESIDUAL, ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE

AUTHOR
Brown, Peter, (LLNL), pnbrown@llnl.gov Hindmarsh, Alan, (LLNL), alanh@llnl.gov Seager, Mark K., (LLNL), seager@llnl.gov Lawrence Livermore National Laboratory PO Box 808, L-60 Livermore, CA 94550 (510) 423-3141

DESCRIPTION
This routine is extracted from the LINPACK routine SGESL with changes due to the fact that A is an upper Hessenberg matrix. SHELS solves the least squares problem: MIN(B-A*X,B-A*X) using the factors computed by SHEQR. *Usage: INTEGER LDA, N REAL A(LDA,N), Q(2*N), B(N+1) CALL SHELS(A, LDA, N, Q, B) *Arguments: A :IN Real A(LDA,N) The output from SHEQR which contains the upper triangular factor R in the QR decomposition of A. LDA :IN Integer The leading dimension of the array A. N :IN Integer A is originally an (N+1) by N matrix. Q :IN Real Q(2*N) The coefficients of the N Givens rotations used in the QR factorization of A. B :INOUT Real B(N+1) On input, B is the right hand side vector. On output, B is the solution vector X.

SEE ALSO
SGMRES

ROUTINES CALLED
SAXPY

REVISION HISTORY (YYMMDD)
871001 DATE WRITTEN
881213 Previous REVISION DATE
890915 Made changes requested at July 1989 CML Meeting. (MKS)
890922 Numerous changes to prologue to make closer to SLATEC standard. (FNF)
890929 Numerous changes to reduce SP/DP differences. (FNF)
910411 Prologue converted to Version 4.0 format. (BAB)
910502 Added C***FIRST EXECUTABLE STATEMENT line. (FNF)
910506 Made subsidiary to SGMRES. (FNF)
920511 Added complete declaration section. (WRB)