[FRIAM] Looking for an algorithm

[Edward Angel]

I remember from my days doing systems and controls that the Kronecker product arises when you extend 1D methods for linear-quadradic problems to 2D. I actually used it in my thesis.

Ed
_______________________

Ed Angel

Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)
Professor Emeritus of Computer Science, University of New Mexico

1017 Sierra Pinon
Santa Fe, NM 87501
505-984-0136 (home)		 	angel at cs.unm.edu <mailto:angel at cs.unm.edu>
505-453-4944 (cell) 				http://www.cs.unm.edu/~angel <http://www.cs.unm.edu/~angel>

> On Nov 4, 2021, at 1:36 PM, Jon Zingale <jonzingale at gmail.com> wrote:
> 
> Thanks to everyone who helped pitch in on this. I was happy to finally track down a pdf of Van Loan & Pitsianis [1993]. As stated in this other article on "Automated Kronecker Product Approximation"[KoPA]:
> 
> "This was introduced in the matrix computation literature as the nearest Kronecker product problem in Van Loan and Pitsianis, who demonstrated its equivalence to the best rank-one approximation and therefore also to the SVD, after a proper rearrangement of the matrix entries."
> 
> As well as:
> 
> "Finding a low-rank approximation of a given matrix is closely related to the singular value decomposition, and the connection was revealed as early as Eckart and Yount (1936)]"
> 
> It is surprising that it took until the 90s for the problem to bite someone and for explicit algorithms to emerge. Also, I am amazed that the body of the literature seems to come from the data sciences, as I arrived at the problem from studying discrete dynamical systems. I am hoping to write up a paper on the connection between them and NKP soon. Would anyone know where I can find a python, C++, or Haskell implementation easily?
> 
> Thanks again for the help.
> 
> [1993] https://www.cs.cornell.edu/cv/ResearchPDF/Approximation%20with%20Kronecker%20Products,%20from%20Linear%20Algebra%20for%20Large%20Scale%20and%20Real-%20Time%20Applications.pdf <https://www.cs.cornell.edu/cv/ResearchPDF/Approximation%20with%20Kronecker%20Products,%20from%20Linear%20Algebra%20for%20Large%20Scale%20and%20Real-%20Time%20Applications.pdf>
> 
> [KoPA] https://arxiv.org/pdf/1912.02392.pdf <https://arxiv.org/pdf/1912.02392.pdf>
> .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn UTC-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives:
> 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/
> 1/2003 thru 6/2021  http://friam.383.s1.nabble.com/

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20211104/e3e4b39a/attachment.html>