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.TH sva 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
sva - singular value approximation
.SH CALLING SEQUENCE
.nf
[U,s,V]=sva(A,k)
[U,s,V]=sva(A,tol)
.fi
.SH PARAMETERS
.TP 8
A
: real or complex matrix
.TP
k
: integer
.TP
tol
: nonnegative real number
.SH DESCRIPTION
Singular value approximation.
.LP
.Vb [U,S,V]=sva(A,k)
with \fVk\fR an integer >=1, returns \fVU,S\fR and \fVV\fR such that
\fVB=U*S*V'\fR is the best L2 approximation
of \fVA\fR with rank(\fVB\fR)=\fVk\fR.
.LP
.Vb [U,S,V]=sva(A,tol)
with \fVtol\fR a real number, returns \fVU,S\fR and \fVV\fR such that
\fVB=U*S*V'\fR such that L2-norm of \fVA-B\fR is at most \fVtol\fR.
.SH EXAMPLE
.nf
A=rand(5,4)*rand(4,5);
[U,s,V]=sva(A,2);
B=U*s*V';
svd(A)
svd(B)
clean(svd(A-B))
.fi
.SH SEE ALSO
svd
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