theory vs. practice

Occasionally, I attend seminars re applied math, 
typically discussing filters, or image processing, 
often involving high dimensional spaces.

The focus is usually the efficiency of the algorithms, 
or their accuracy, e.g. voice recognition.  Of course 
they also try to prove theoretical correctness. 

And there's the problem, in my view.  They throw 
around gradients and conjugate gradients and 
Laplacians cavalierly.  Which is perfectly valid 
theoretically, but numerically, doesn't this raise 
concerns?  Isn't there a vast literature on the 
numerical difficulties in implementation?  
Especially for derivatives.  But they say "no sweat, 
it's one line in MATLAB!"

??
Is my skepticism justified, or am I beating a 
dead horse?  Granted that I'm not a real expert 
in the fine points - 

--
Rich

On Tuesday, May 6, 2014 3:40:30 PM UTC+12, RichD wrote:
> Occasionally, I attend seminars re applied math, 
> 
> typically discussing filters, or image processing, 
> 
> often involving high dimensional spaces.
> 
> 
> 
> The focus is usually the efficiency of the algorithms, 
> 
> or their accuracy, e.g. voice recognition.  Of course 
> 
> they also try to prove theoretical correctness. 
> 
> 
> 
> And there's the problem, in my view.  They throw 
> 
> around gradients and conjugate gradients and 
> 
> Laplacians cavalierly.  Which is perfectly valid 
> 
> theoretically, but numerically, doesn't this raise 
> 
> concerns?  Isn't there a vast literature on the 
> 
> numerical difficulties in implementation?  
> 
> Especially for derivatives.  But they say "no sweat, 
> 
> it's one line in MATLAB!"
> 
> 
> 
> ??
> 
> Is my skepticism justified, or am I beating a 
> 
> dead horse?  Granted that I'm not a real expert 
> 
> in the fine points - 
> 
> 
> 
> --
> 
> Rich

I'm not so sure many of the more academic algorithms find there way into embedded devices because they are just too big to fit in! Certainly there is limited vocab speech recognisers but searching though hundreds of thousands of classification types would be reserved for a bigger machine! I  suppose in principle if you have the time and money you could just about do anything you like but they won't be products, just one-offs. You need a lot of off-line tests if you are using fixed-point arithmetic too. (FPGAs).

On Mon, 5 May 2014 23:25:20 -0700 (PDT), gyansorova@gmail.com wrote:

>I'm not so sure many of the more academic algorithms find there way 
>into embedded devices because they are just too big to fit in! 

On the other hand, technology marches on. I developed some audio
algorithms in the early 1990s that I expected would never be
implementable within my lifetime. Nowadays I can run them on an ARM in
real time.

Greg

I can tell you from personal experience that gradients, conjugate gradients, and Laplace are used in lots of systems, even very small microPICs. It's good to be skeptical, but don't underestimate the willingness of engineers to get things working. 

If you constrain your research only to what you subjectively think is realistic for the present implementation fabric, we won't have half the nice things we have today. 

On Monday, May 5, 2014 10:40:30 PM UTC-5, RichD wrote:
.......Which is perfectly valid 
> theoretically, but numerically, doesn't this raise 
> concerns?> 
>
> Rich

ABSOLUTELY! A couple of examples: The normalized LMS will diverge if you don't take into account the possibility that the variance of the input can approach 0. For Gaussian elimination of linear systems, the algorithm could diverge if the pivot approaches 0 (because of this, Matlab checks the value of the pivot and performs a row exchange if it is below a minimum value). Fixed-point arithmetic can be a big problem. Etc, etc., etc........

julius wrote:
> I can tell you from personal experience that gradients, conjugate gradients, and Laplace are used in lots of systems, even very small microPICs. It's good to be skeptical, but don't underestimate the willingness of engineers to get things working.
>
> If you constrain your research only to what you subjectively think is realistic for the present implementation fabric, we won't have half the nice things we have today.
>

LOL
If my father was still alive he would have fun expanding on that 
last paragraph.
When he was taking a BSME in mid-20's, he took a course titled 
"Applicable Math". They couldn't title it "Applied Math" as 
hardware wouldn't exist for decades. When I attempted a BSEE in 
early-60's, operational amplifiers had cook books available.

That sounds like a great company name: "Applicable Technologies, Inc."!

On Tue, 6 May 2014 11:37:37 -0700 (PDT), julius <juliusk@gmail.com>
wrote:

>That sounds like a great company name: "Applicable Technologies, Inc."!

Or their supplier, "Available Materials, Inc."


Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

On Tue, 06 May 2014 19:56:14 GMT
eric.jacobsen@ieee.org (Eric Jacobsen) wrote:

> On Tue, 6 May 2014 11:37:37 -0700 (PDT), julius <juliusk@gmail.com>
> wrote:
> 
> >That sounds like a great company name: "Applicable Technologies, Inc."!
> 
> Or their supplier, "Available Materials, Inc."
> 
> 
> Eric Jacobsen
> Anchor Hill Communications
> http://www.anchorhill.com

Funny, recently all of my suppliers have decided to be Unavailable Materials, Inc.

-- 
Rob Gaddi, Highland Technology -- www.highlandtechnology.com
Email address domain is currently out of order.  See above to fix.

Did they try to sell you some Unobtainium?