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<HTML>
<HEAD><TITLE>SB04RY - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="SB04RY">SB04RY</A></H2>
<H3>
Solving a system of equations in Hessenberg form with one right-hand side
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To solve a system of equations in Hessenberg form with one
right-hand side.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE SB04RY( RC, UL, M, A, LDA, LAMBDA, D, TOL, IWORK,
$ DWORK, LDDWOR, INFO )
C .. Scalar Arguments ..
CHARACTER RC, UL
INTEGER INFO, LDA, LDDWOR, M
DOUBLE PRECISION LAMBDA, TOL
C .. Array Arguments ..
INTEGER IWORK(*)
DOUBLE PRECISION A(LDA,*), D(*), DWORK(LDDWOR,*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
RC CHARACTER*1
Indicates processing by columns or rows, as follows:
= 'R': Row transformations are applied;
= 'C': Column transformations are applied.
UL CHARACTER*1
Indicates whether A is upper or lower Hessenberg matrix,
as follows:
= 'U': A is upper Hessenberg;
= 'L': A is lower Hessenberg.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
M (input) INTEGER
The order of the matrix A. M >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,M)
The leading M-by-M part of this array must contain a
matrix A in Hessenberg form.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,M).
LAMBDA (input) DOUBLE PRECISION
This variable must contain the value to be multiplied with
the elements of A.
D (input/output) DOUBLE PRECISION array, dimension (M)
On entry, this array must contain the right-hand side
vector of the Hessenberg system.
On exit, if INFO = 0, this array contains the solution
vector of the Hessenberg system.
</PRE>
<B>Tolerances</B>
<PRE>
TOL DOUBLE PRECISION
The tolerance to be used to test for near singularity of
the triangular factor R of the Hessenberg matrix. A matrix
whose estimated condition number is less than 1/TOL is
considered to be nonsingular.
</PRE>
<B>Workspace</B>
<PRE>
IWORK INTEGER array, dimension (M)
DWORK DOUBLE PRECISION array, dimension (LDDWOR,M+3)
The leading M-by-M part of this array is used for
computing the triangular factor of the QR decomposition
of the Hessenberg matrix. The remaining 3*M elements are
used as workspace for the computation of the reciprocal
condition estimate.
LDDWOR INTEGER
The leading dimension of array DWORK. LDDWOR >= MAX(1,M).
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
= 1: if the Hessenberg matrix is (numerically) singular.
That is, its estimated reciprocal condition number
is less than or equal to TOL.
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE>
None.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
None
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
</PRE>
<B>Program Results</B>
<PRE>
None
</PRE>
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