software.jemdoc

# jemdoc: eqsize{200}
= SLRA: Software for structured low-rank approximation
[http://homepages.vub.ac.be/~imarkovs/ Ivan Markovsky] ([imarkovs@vub.ac.be]) 
and 
[http://homepages.vub.ac.be/~kusevich/ Konstantin Usevich] ([kusevich@vub.ac.be]) 

The package computes locally optimal solutions to low-rank approximation problems 
\(
minimize \quad over \ \widehat p \quad ||p - \widehat p||_w \quad subject \ to \quad rank({\cal S}(\widehat p)) \leq r 
\)
with the following features:
- mosaic Hankel structured approximating matrix ${\cal S}(\widehat p)$,
- weighted 2-norm approximation criterion $||\cdot||_w$,
- fixed elements in the approximating matrix,
- missing elements in the data matrix, and
- linear constraints on an approximating matrix's left kernel basis.

For an $m\times n$ data matrix, with $m < n$, the computational complexity of the cost function and derivative evaluation is $O(m^2n)$, so that the package is suitable for applications with $n\gg m$.

== [slra.pdf Documentation]

== [slra.tgz Download] 
- [https://github.com/slra/slra source code]

== Citing

~~~
{}{}
@TechReport{slra-software,
  author = 	 {I. Markovsky and K. Usevich},
  title = 	 {Software for weighted structured low-rank approximation},
  institution =  {Univ. of Southampton},
  year = 	 {2012},
  number = 	 {339974},
  address =      {\url{http://eprints.soton.ac.uk/339974}},
}
~~~

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