sci.math.num-analysis Google Group

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Re: PDEs Involving Absolute Value

he...@alumni.brown.edu (Greg Heath) — Fri, 11 Nov 2009 22:43:37 UT

You may mean. -1 <= C <= 1.
However, even then it is not true.
It depends on the application. For example, the Fourier Series
representation of any piecewise continuous function converges
to the average of the right and left hand limits.
I cannot think of any uniform approximator for which this is not true.

Re: Numerical derivative of matrix eqn

spasm...@gmail.com (spasmous) — Fri, 11 Nov 2009 19:03:48 UT

Yes, its clear I made an incorrect assumption about b*pinv(b). Thanks,
I should have noticed that myself! Thanks for your replies BTW, I'm
really happy this group is still alive to post questions. It looks
almost overrun with spam lately.

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Re: Numerical derivative of matrix eqn

he...@alumni.brown.edu (Greg Heath) — Fri, 11 Nov 2009 17:41:52 UT

On Nov 27, 11:02 am, spellu...@fb04633.mathematik.t u-darmstadt.de
Thanks for getting to the heart of the matter.
On Nov 27, 11:02 am, spellu...@fb04633.mathematik.t u-darmstadt.de
Thanks for getting to the heart of the matter.
Examples:
clear all, clc
A = [1 2; 3 4; 5 6] ;
b = [1;2;3] ;
db = [1e-2;1e-2;1e-2] ;

Re: PDEs Involving Absolute Value

aruzin...@general-cathexis.com (aruzinsky) — Fri, 11 Nov 2009 17:01:13 UT

On Nov 27, 10:01 am, spellu...@fb04633.mathematik.t u-darmstadt.de
How "seemingly"? There are no exact minimum L1 norm results to
compare. For all you know, the author's false solutions are MORE
visually appealing than the exact solutions. But, then he would have
a very hard time explaining it, huh?

Re: Numerical derivative of matrix eqn

spellu...@fb04633.mathematik.tu-darmstadt.de (Peter Spellucci) — Fri, 11 Nov 2009 16:02:36 UT

In article <34d21c55-0c55-44cb-b5fc-3c96d 846b...@p35g2000yqh.googlegrou ps.com>,
you assume that b*pinv(b) = id
hth
peter

Re: PDEs Involving Absolute Value

aruzin...@general-cathexis.com (aruzinsky) — Fri, 11 Nov 2009 16:02:24 UT

There is no such word as "civilianly" but I will civilly tell you that
sgn(x) can be replaced by an infinite number of functions f(x) in your
equations satisfying.
f(x) = -1, x<0
f(x) = 1, x>0
f(x) = C, x=0, -oo<C<oo
and, yet, using different C would likely affect the stationary points
in the aforementioned steepest descent. And, let's make it perfectly

Re: PDEs Involving Absolute Value

spellu...@fb04633.mathematik.tu-darmstadt.de (Peter Spellucci) — Fri, 11 Nov 2009 16:01:31 UT

In article <d4d37c37-0516-4725-8126-9c8f5 c6ae...@b2g2000yqi.googlegroup s.com>,
aaaah, no I see the sense behind your original question, but you had better
wrote in your initial contribution what you wrote here.
Concerning the paper you pointed too: yes, there are errors
(the gradient of the l1-norm is indeed quite funny)

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Re: Numerical derivative of matrix eqn

he...@alumni.brown.edu (Greg Heath) — Fri, 11 Nov 2009 04:46:52 UT

clear all, clc
A = [1 2; 3 4; 5 6] ;
b = [1;2;3] ;
db = [1e-2;1e-2;1e-2] ;
pinvA = pinv(A)
x = pinvA*b
dx = pinvA*db
err = A*x-b
% pinvA =
% -1.3333 -0.3333 0.6667
% 1.0833 0.3333 -0.4167
% x =
% 0.0000
% 0.5000
% dx =
% -0.0100
% 0.0100
% err =
% 1.0e-015 *