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nokia8650
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Is there any general formula for interval bisection, rather than consider two similar triangles each time?
Thanks
Thanks
The general formula for interval bisection is:
xn+1 = (xn-1 + xn) / 2,
where xn is the nth approximation of the root or midpoint of the interval.
The interval bisection method involves dividing a given interval into two equal parts and then checking which part contains a root of the function. This process is repeated until the interval becomes small enough to approximate the root with a desired level of accuracy.
No, the interval bisection method is not guaranteed to find the root of a function. It can only find a root if the function is continuous and changes sign within the given interval. If these conditions are not met, the method may fail to converge or may converge to a wrong root.
Interval bisection is a relatively simple and straightforward method, making it easy to implement and understand. It is also guaranteed to converge if the conditions are met. Additionally, it does not require the function to be differentiable, making it suitable for a wider range of functions.
One limitation of the interval bisection method is that it can be slow to converge, especially if the initial interval is large or if the root is located near the endpoints of the interval. It also requires the function to be continuous, which may not always be the case. In these situations, other root-finding methods may be more efficient.