Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sdd.hp.com!usc!apple!agate!shelby!portia.stanford.edu!elaine3.stanford.edu!mcgrant From: mcgrant@elaine3.stanford.edu (Michael Grant) Newsgroups: comp.sys.handhelds Subject: Re: the search for the godlike handheld Summary: consider the expense of such godlike-ness Keywords: do it another way Message-ID: <1990Nov15.000438.13116@portia.Stanford.EDU> Date: 15 Nov 90 00:04:38 GMT References: Sender: mcgrant@portia.stanford.edu (Michael Charles Grant) Organization: Stanford University - AIR Lines: 43 In article bagchi@eecs.umich.edu (Ranjan Bagchi) writes: > I'm looking for something to replace my HP28C. It's logical, I >guess, to go to a 48SX. One problem, tho. One of my main beefs with >the 28 is that I can't have variables in a vector or matrix. It's >variable. Didn't work. > So...is there any plans in the work to put this into the >matrix operations? It really doesn't make much sense, at least to me. Well, it certainly would be awfully nice to have symbolic matrix operations. For example, I would like to be able to calculate (sI-A)^-1 almost daily. However, have you considered how much MORE programming that would require to do such a thing? The fact of the matter is that I am more than impressed with the amount of symbolic math that the HP calculators do, and we tend to get spoiled into expecting more! Perhaps a program designed for a more powerful system--like Mathematica-- could handle such functions. But, the on the HP48sx it would simply be too slow and require too much ROM space to support symbolic matrices, in my opinion. On the other hand, depending on what you are doing, there are often ways around such a limitation. Take my example of (sI-A)^-1, often called the _resolvent_ of A. Well, this matrix is the Laplace transform of exp(At), and this turns out to be quite useful in a lot of ways. So, people have come up with many ways to calculate the resolvent without resorting to the slow, symbolic computation of Adj(sI-A)/det(sI-A). Thanks to one particular formula, in fact, I have developed precisely such a program, which does calculations no more complicated than matrix multiplication, and produces a very accurate result QUICKLY (~3 seconds or so for a 4x4 in FAST mode). In addition, there have been symbolic matrix manipulation programs floating around that use the list data structure of the HP. I imagine that they are slow, but if push comes to shove you could use those. So, the HP48sx is probably your best bet if you want to do ANYTHING with matrices, and this probably includes symbolic matrix manipulation as well. If you NEED something more powerful still, you'll need a full-blown computer. One matrix-user's opinion, Michael C. Grant mcgrant@portia.edu (If anyone wants that resolvent program, e-mail me...I have a corollary program that calculates c(sI-A)^-1b as well, even for multi-input, multi- output systems...)