Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!usc!merlin.usc.edu!usc.edu!raulmill From: raulmill@usc.edu (Raul Deluth Rockwell) Newsgroups: comp.lang.apl Subject: Re: Syntax for extended matrix operations Message-ID: Date: 6 Dec 89 05:42:08 GMT References: <539@s5.Morgan.COM> Sender: news@merlin.usc.edu Organization: University of Southern California, Los Angeles, CA Lines: 20 In-reply-to: amull@Morgan.COM's message of 27 Nov 89 05:27:10 GMT In article <539@s5.Morgan.COM> amull@Morgan.COM (Andrew P. Mullhaupt) writes: I would like to solicit suggestions for primitives to be added to the APL lexicon which would update the representation of linear algebraic concepts. In particular I have in mind a way to deal with the concept of matrix factorizations; Cholesky, QR, and SVD. The point is that if you use quad-divide, you have to factor the matrix every time you come up with a right hand side (left hand side in APL terms) that needs evaluating. Seems to me that factorization tends to yield multiple results. This could be dealt with by 'inventing' a new type, but how much would be saved by this approach? Comparing factorization with Guass-Jordan reduction, how many operations are saved over the course of an algorithm? (Assume some sort of ideal efficiency in the implementation of factorization). I suppose I ought to do some of this myself, but I don't know what kind of algorithms you are trying to optimize. --