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) an...@cs.unm.edu <mailto:an...@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 <jonzing...@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/
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