I have found a polynomial time solution of an NPC problem. My algorithm give exact result in most cases. For example if I run my algorithm for 20000 problem instances, then it fails 10 times to give correct result. But, I am unable to prove the approximation ratio mathematically. Is it feasible to show it with the experimental results? I am waiting to hear the possible solutions for it.
Is it feasible to show it with the experimental results?
No, you can not. There is no shortcut around formal proofs here.
First of all, any more information to give about the problem? Your algorithm? These sorts of things would make a question such as this far more approachable.
In what sense are you unable to prove it? I think a theoretical result is far stronger than any experimental results you may be able to gather, since it demonstrates that, without fail, your algorithm will return a solution with a value within some constant factor of the optimal for any given instance of the problem. The instances of the problem that your algorithm fails to give a answer for, do you notice any trends in terms of how 'off' the results are?