Discussion: Introducing new operators for matrix computation

Huaiyu Zhu hzhu at localhost.localdomain
Mon Jul 17 02:34:01 EDT 2000


On Mon, 17 Jul 2000 02:07:08 GMT, jepler epler <jepler.lnk at lnk.ispi.net> wrote:
>On Sat, 15 Jul 2000 04:29:09 GMT, Huaiyu Zhu
> <hzhu at localhost.localdomain> wrote:
>>That's the beauty of numerical computation, because all kinds of
>>applications, from animation on your screen to controlling satallite in
>>space to analysing molecular structures to calculating consumer preference
>>could all be expressed in the language of linear algebra.  (Mathematicians
>>study spaces more abstract than linear spaces, but you wouldn't want to hear
>>about them before appreciating the usefulness of linear algebra.) For
>>example, all deterministic procedures are functions, and most functions we
>>see are simply points in an (infinite dimensional) space.
>
>That's the beauty of procedural programming, because all kinds of
>applications, from animation on your screen to controlling a satellite in
>space to analyzing molecular structures to calculating consumer preference
>could all be expressed in the language of procedural programming.
>(Programmers study programming languages more abstract than functional
>programming, but you wouldn't want to hear about them before appreciating
>the usefulness of procedural programming.)  For example, all deterministic
>processes are expressible as Turing machines, and most turing machines
>we see are simply expressible in procedural languages.
>

The first paragraph was a response to a particular argument.  There are
problems that most people would not think of using linear algebra and ends
up with programs of hundreds of lines with slow for loops, but which could
be expressed in just a couple of math formula and, given the right syntax,
maps to less than a dozen lines of short clean code.

I'm not sure what the second paragraph is referring to.  If it is telling
people that something that's written in assembly could be easily done in
procedural languages then it makes perfect sense, except for the reference
to Turing machines - if you use Turing machines as building blocks (as
opposed to computing engines), how many TMs do you expect to halt before the
program finishes?

not-that-this-is-on-topic-ly yr's

Huaiyu

PS. I'm sure someone would ask how you could complete the calculation of an
infinite dimensional vector.  That is left as an exercise to the reader. :-)



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