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<HTML>
<HEAD><TITLE>MB02TD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB02TD">MB02TD</A></H2>
<H3>
Estimation of the reciprocal condition number of an upper Hessenberg matrix
</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 estimate the reciprocal of the condition number of an upper
Hessenberg matrix H, in either the 1-norm or the infinity-norm,
using the LU factorization computed by MB02SD.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB02TD( NORM, N, HNORM, H, LDH, IPIV, RCOND, IWORK,
$ DWORK, INFO )
C .. Scalar Arguments ..
CHARACTER NORM
INTEGER INFO, LDH, N
DOUBLE PRECISION HNORM, RCOND
C .. Array Arguments ..
INTEGER IPIV( * ), IWORK( * )
DOUBLE PRECISION DWORK( * ), H( LDH, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
NORM CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix H. N >= 0.
HNORM (input) DOUBLE PRECISION
If NORM = '1' or 'O', the 1-norm of the original matrix H.
If NORM = 'I', the infinity-norm of the original matrix H.
H (input) DOUBLE PRECISION array, dimension (LDH,N)
The factors L and U from the factorization H = P*L*U
as computed by MB02SD.
LDH INTEGER
The leading dimension of the array H. LDH >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix
was interchanged with row IPIV(i).
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix H,
computed as RCOND = 1/(norm(H) * norm(inv(H))).
</PRE>
<B>Workspace</B>
<PRE>
IWORK INTEGER array, dimension (N)
DWORK DOUBLE PRECISION array, dimension (3*N)
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
An estimate is obtained for norm(inv(H)), and the reciprocal of
the condition number is computed as
RCOND = 1 / ( norm(H) * norm(inv(H)) ).
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
-
</PRE>
<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE> 2
The algorithm requires 0( N ) operations.
</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>
<HR>
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