[Date Index]
[Thread Index]
[Author Index]
regularize a function (proof function)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg72404] regularize a function (proof function)
*From*: Wiso <giurrerotipiacerebbe at hotmailtipiacerebbe.itipiacerebbe>
*Date*: Mon, 25 Dec 2006 04:52:45 -0500 (EST)
I want to regularize a function, I want that it is C^inf and with
compact support (proof function for distributions).
I start with:
a = -1; b = 1;
theta[x_] := (-x^2) + 1
f[x_] := If[x < b && x > a, theta[x], 0]
Plot[f[x], {x, -2, 2}];
Now f[x] is with compact support, but it's not C^inf. I do:
phi[epsilon_, x_] := If[x >=epsilon || x
<= (-epsilon), 0, Exp[(-epsilon^2)/((epsilon^2 - x^2))]])
Plot[phi[1,x],{x,-1,1}];
this is a proof function. I define
g[epsilon_, x_] := (Int[phi[epsilon, Abs[x - y]] f[y] {y,-inf,inf}]) /
(Int[phi[epsilon, Abs[y]] {y,-inf,inf}])
Now I want to see it:
Plot[g[1,x],{x,-2,2}]
It has a loss of precision, how can I solve it?
Prev by Date:
**StoppingTest options (need help)**
Next by Date:
**RE: CAD/CAM**
Previous by thread:
**Re: StoppingTest options (need help)**
Next by thread:
**Re: regularize a function (proof function)**
| |