Using matlab function limit - matlab not able to calculate

Hi, I have a function:

f(k)=(e^(A^T+h*E_ij)-e^(t*A^T))/h

I want to send h to 0.

Variable for testing: A = [0 1 2 3; -1 0 -2 -3; 4 0 8 9; -6 -7 8 0]; i= 2; j= 3; t= 2;

my function:

"function f = gradA(k)

i=evalin('base','i'); % i is number in {1,2,3,4}

j=evalin('base','j'); % j is number in {1,2,3,4}

E=zeros(4,4);

E(i,j)=1; % E is real 4x4-Matrix, where all entries are 0, entry (i,j) is 1

A=evalin('base','A'); % A is real 4x4-Matrix

t=evalin('base','t'); % t is number in {1,2,...k,}

f=(expm ( t* (transpose(A)) + k*E) - expm(t*transpose(A)))/k;"

I run in matlab:

> syms k

> limit(gradA(k),k,0,'right')

But Matlab not able to calculate the limit - endless running. Any suggestion how to make it work? The limit is supposed to be existent in theory.

[Walter Roberson]

For heaven's sake, if you need the value of i and j in the function then pass those variables in rather than using evalin('base') to fetch them!

[Michael S]

You might be right, though, this should not be the problem. I did not want to confuse limit() with further parameters.

[Walter Roberson]

What is T ? Or does A^T indicate transposing A in your notation ? If it does then why not skip the transpose and define a new already-transposed array ?

[Michael S]

T means transposed matrix. I tried the same with an already-transposed array. Did not change the outcome.

[Walter Roberson]

Is there even a mathematical proof that there must be a limit ?

[Michael S]

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6830

Page 11

[Walter Roberson]

Reading that, I would think it quite unlikely that MATLAB would be able to derive the limit.

[Michael S]

Ok, fair enough. At least the function is implemented correctly. With the rest I have to live. Thank you very much for your help