SHEQR(3)

SYNOPSIS
SUBROUTINE SHEQR (A, LDA, N, Q, INFO, IJOB)

NAME
sheqr - Internal routine for SGMRES.

LIBRARY
SLATEC (SLAP)

CATEGORY
D2A4, D2B4

TYPE
SINGLE PRECISION (SHEQR-S, DHEQR-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 performs a QR decomposition of an upper Hessenberg matrix A using Givens rotations. There are two options available: 1) Performing a fresh decomposition 2) updating the QR factors by adding a row and a column to the matrix A. *Usage: INTEGER LDA, N, INFO, IJOB REAL A(LDA,N), Q(2*N) CALL SHEQR(A, LDA, N, Q, INFO, IJOB) *Arguments: A :INOUT Real A(LDA,N) On input, the matrix to be decomposed. On output, the upper triangular matrix R. The factorization can be written Q*A = R, where Q is a product of Givens rotations and R is upper triangular. LDA :IN Integer The leading dimension of the array A. N :IN Integer A is an (N+1) by N Hessenberg matrix. Q :OUT Real Q(2*N) The factors c and s of each Givens rotation used in decomposing A. INFO :OUT Integer = 0 normal value. = K if A(K,K) .eq. 0.0 . This is not an error condition for this subroutine, but it does indicate that SHELS will divide by zero if called. IJOB :IN Integer = 1 means that a fresh decomposition of the matrix A is desired. will be updated by the addition of a row and a column.

SEE ALSO
SGMRES

ROUTINES CALLED
(NONE)

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)
910506 Made subsidiary to SGMRES. (FNF)
920511 Added complete declaration section. (WRB)