I come from Computer Science and I designed an algorithm belongs to Numerical Linear Algebra field. The analysis of algorithms in Computer Science usually involves the correctness, time and space complexity.
Some one told me this algorithm is presentable and publishable as a paper if you can prove that it is numerically stable. Some thing we have never done before and I don't know where to start from!. All I know is if I impose some perturbation to variables, the results must be good!
The algorithm involves a for loop, in each loop it computes determinant of a symmetric Jacobi matrix and it has some plus and minus and power 2 and division operations.
How can I show that this algorithm is numerically stable?
I am not sure if this information is enough, if any other thing is needed I will provide it.
Thanks in advance.