I'm trying to evaluate the numerical stability of LU decomposition. I implemented code in java to calculate the inverse matrix with LU. I made 3 attemps. a) mantissa 4 b) mantissa 6 c) maschine accuracy
a and b use a method to round the values of each step to the given mantissa. If i compare my results, the values of a and b are similar. But differ in value in a range of 20 to 1000. Both are not even close to the result of attemp c. But c is very close to a result calculated by mathematica. So I think the implementation is correct. But if I go down with mantissa from 16 to 6 in steps of 1, the result changes dramaticly. How do I evaluate the LU decomposition? It seems very unstable to me. But what are the reasons for such a behavior?
Sincerly, Heinz