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<HTML>
<HEAD><TITLE>SB04MU - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="SB04MU">SB04MU</A></H2>
<H3>
Constructing and solving a linear algebraic system whose coefficient matrix (stored compactly) has zeros below the second subdiagonal
</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 construct and solve a linear algebraic system of order 2*M
whose coefficient matrix has zeros below the second subdiagonal.
Such systems appear when solving continuous-time Sylvester
equations using the Hessenberg-Schur method.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
SUBROUTINE SB04MU( N, M, IND, A, LDA, B, LDB, C, LDC, D, IPR,
$ INFO )
C .. Scalar Arguments ..
INTEGER INFO, IND, LDA, LDB, LDC, M, N
C .. Array Arguments ..
INTEGER IPR(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), D(*)
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
</PRE>
<B>Input/Output Parameters</B>
<PRE>
N (input) INTEGER
The order of the matrix B. N >= 0.
M (input) INTEGER
The order of the matrix A. M >= 0.
IND (input) INTEGER
IND and IND - 1 specify the indices of the columns in C
to be computed. IND > 1.
A (input) DOUBLE PRECISION array, dimension (LDA,M)
The leading M-by-M part of this array must contain an
upper Hessenberg matrix.
LDA INTEGER
The leading dimension of array A. LDA >= MAX(1,M).
B (input) DOUBLE PRECISION array, dimension (LDB,N)
The leading N-by-N part of this array must contain a
matrix in real Schur form.
LDB INTEGER
The leading dimension of array B. LDB >= MAX(1,N).
C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
On entry, the leading M-by-N part of this array must
contain the coefficient matrix C of the equation.
On exit, the leading M-by-N part of this array contains
the matrix C with columns IND-1 and IND updated.
LDC INTEGER
The leading dimension of array C. LDC >= MAX(1,M).
</PRE>
<B>Workspace</B>
<PRE>
D DOUBLE PRECISION array, dimension (2*M*M+7*M)
IPR INTEGER array, dimension (4*M)
</PRE>
<B>Error Indicator</B>
<PRE>
INFO INTEGER
= 0: successful exit;
> 0: if INFO = IND, a singular matrix was encountered.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
A special linear algebraic system of order 2*M, whose coefficient
matrix has zeros below the second subdiagonal is constructed and
solved. The coefficient matrix is stored compactly, row-wise.
</PRE>
<A name="References"><B><FONT SIZE="+1">References</FONT></B></A>
<PRE>
[1] Golub, G.H., Nash, S. and Van Loan, C.F.
A Hessenberg-Schur method for the problem AX + XB = C.
IEEE Trans. Auto. Contr., AC-24, pp. 909-913, 1979.
</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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