问题
I'm currently in a Java class at my university and we've been asked to code a Taylor Series equation to compute a Sine function. I've coded what makes sense to me, and I've tried debugging every section of code I can think of to make sure all of the parts are functioning the way I think they should, but the program still isn't functioning right. So, I'm hoping someone might look at this and spot what I'm doing wrong.
this is the equation: Taylor Series Equation
public class Sine {
public static int factorial(int a) {
int num = a;
if (a == 1) return 1;
for (int i = 1; i < num; i++){
a = a * i;
} return a;
}
public static double numerator(double x, int power) {
double ret = Math.pow(x, power);
return ret;
}
public static void main(String[] args) {
int power = 1;
int iter = 0;
double x = Math.PI/4;
int sign = 1;
while (iter != 10) {
iter++;
System.out.println("Iteration " + iter + ": " + x);
x += sign * numerator(x, power)/factorial(power);
power += 2;
sign *= -1;
}
System.out.println("\nTaylor Series, Final: " + x);
System.out.println("Value of Sine: " + Math.sin(Math.PI/4));
}
}
I'm just very confused what's going on and why it's not working.
回答1:
What you're doing wrong (thanks @AndyTurner) is trying to store large factorials in an int
, which of course can only store numbers up to about 2 billion.
To avoid having to deal with large numbers and their limited accuracies, you could use the following principle, that applies to the Taylor series for sines.
Term in xn = (Term in xn-2)
* - x * x / n / (n-1)
.
For example, if you've already calculated x5 / 5!, then the best way to calculate -x7 / 7! is to multiply the number you've already calculated by -x2 / 6 / 7.
If you calculate your terms this way, then add them up, you avoid all the problems that come with dealing with large numbers.
来源:https://stackoverflow.com/questions/44813627/taylor-series-of-a-sine