- #1
Silviu
- 624
- 11
Homework Statement
Hello! I am not sure if this is the best place to ask this question, but I need some help. So i use the bisection method to find the zeros of a function. When I do it for sin(x), with the initial interval being ##[10^6 \pi, (10^6+1) \pi]##, the program enters an infinite loop if the ending criteria is ##\frac{b-a}{2}<10^{-10}##, where a and b are the limits of the interval. I need to explain why does this happen, while if I use instead of ##10^{-10}##, let’s say ##10^{-8}##, it works. I am aware it is related to the loss of significance, as the ##10^6 \pi## and ##(10^6+1) \pi## are very close to each other, so when subtracting may digits are loss, but I am not sure how to explain it completely. Any idea? Thank you!