Function approximation with Maclaurin series
- by marines
I need to approx (1-x)^0.25 with given accuracy (0.0001 e.g.). I'm using expansion found on Wikipedia for (1+x)^0.25. I need to stop approximating when current expression is less than the accuracy.
long double s(long double x, long double d) {
long double w = 1;
long double n = 1; // nth expression in series
long double tmp = 1;
// sum while last expression is greater than accuracy
while (fabsl(tmp) >= d) {
tmp *= (1.25 / n - 1) * (-x); // the next expression
w += tmp; // is added to approximation
n++;
}
return w;
}
Don't mind long double n. :P This works well when I'm not checking value of current expression but when I'm computing 1000 or more expressions. Domain of the function is <-1;1 and s() calculates approximation well for x in <-1;~0.6. The bigger the argument is the bigger is the error of calculation. From 0.6 it exceeds the accuracy.
I'm not sure if the problem is clear enough because I don't know English math language well. The thing is what's the matter with while condition and why the function s() doesn't approximate correctly.
