Message Boards Message Boards


Find the inverse of function h by a numerical way ?

Posted 4 months ago
6 Replies
3 Total Likes

Hello guys, Please I have a question: I need to know the inverse of function "h= a + Q" defined as follows:

(*Définit la fonction indicatrice*)
indicator[x_] := Piecewise[{{1, 0 < x < \[Pi]/2}}, 0];
(*Semi groupe*)
S[x_, t_] := Sum[ Exp[- t  n^2] Integrate[x Sin[s n^2], {s, 0, \[Pi]}]  Sin[x n^2], {n, 5}]
(*controllability map*)
G[x_, t_] := indicator[x] S[x, T - t]
(*Grammian operator Q*)
Q[x_, t_] := (indicator[x])^2  Integrate[(S[x, T - s])^2, {s, T - l, T}]
v[x_, t_] := InverseFunction[a + Q][x, t];
N[v[w1 - S[1, T], T] ]

It's not working for me because of the expression of "h=a + Q" which is complicated

Best regards,

6 Replies
Posted 4 months ago

You can try something like this as long as h has a single value in the inverse domain.

Using Sin as an example

data = Table[{N@Sin[x], x}, {x, 0, Pi/2, Pi/200}];
invF = Interpolation[data];

invF[1/Sqrt[2]] / Degree
(* 45. *)

Sin[45 Degree]
(* 1/Sqrt[2] *)
Posted 4 months ago

Hi Rohit, I just edit my question, I specified the expression of the function to inverse! Do you have any idea why it's not working pleas?

To obtain proper help, show the h function in code or attached a notebook.

Posted 4 months ago

ok, I just edit my question.

Posted 4 months ago

This seems to be the same question as this.

Posted 4 months ago

Indeed yes, I have just checked it is my partner in this work who asked the question, I will send him a message so that he deletes this message not to repeat the same question.

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract