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<H2><A Name="MB02RD">MB02RD</A></H2>
<H3>
Solution of a system of linear equations with upper Hessenberg matrix
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<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>
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<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
To solve a system of linear equations
H * X = B or H' * X = B
with an upper Hessenberg N-by-N matrix H using the LU
factorization computed by MB02SD.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE MB02RD( TRANS, N, NRHS, H, LDH, IPIV, B, LDB, INFO )
C .. Scalar Arguments ..
CHARACTER TRANS
INTEGER INFO, LDB, LDH, N, NRHS
C .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION B( LDB, * ), H( LDH, * )
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<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
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<B>Mode Parameters</B>
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TRANS CHARACTER*1
Specifies the form of the system of equations:
= 'N': H * X = B (No transpose)
= 'T': H'* X = B (Transpose)
= 'C': H'* X = B (Conjugate transpose = Transpose)
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<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix H. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of
columns of the matrix B. NRHS >= 0.
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 from MB02SD; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).
B (input/output) DOUBLE PRECISION array, dimension
(LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB INTEGER
The leading dimension of the array B. LDB >= max(1,N).
</PRE>
<B>Error Indicator</B>
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INFO (output) INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
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<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
The routine uses the factorization
H = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (and one nonzero subdiagonal), and U is upper
triangular.
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<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
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-
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<A name="Numerical Aspects"><B><FONT SIZE="+1">Numerical Aspects</FONT></B></A>
<PRE> 2
The algorithm requires 0( N x NRHS ) operations.
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<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
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None
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<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
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<B>Program Text</B>
<PRE>
None
</PRE>
<B>Program Data</B>
<PRE>
None
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<B>Program Results</B>
<PRE>
None
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