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I am looking for some source that could teach me how bisection method algorithm work in two-variable scalar-valued functions. I found some videos on youtube that didn't really help me understand clear.

I would appreciate if anyone could recommend something to help me out with this topic. It could be anything; tutorial videos, textbooks etc.

Will Ness
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Eldoar
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    What is the direct goal, do you have one function in two variables and want to locate the level curves, or do you have two functions and want to find the solution points of the system? You are aware that even among the root-bracketing methods the bisection method is, while simple to understand, the worst method in terms of computation time? Also, the opposite-sign certificate for the existence of a root would need to be replaced by a winding-number or other index certificate. For polynomials, bisection-exclusion methods exist, branch-and-bound (using interval arithmetic) is another keyword. – Lutz Lehmann Aug 17 '22 at 09:08
  • I want to find x and y which are real numbers and are in the form f(x,y)=0. I know that it might not be the best method for finding roots but I was curious about how it works for functions with two variable. And what does the algorithm look like – Eldoar Aug 20 '22 at 06:41
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    For a scalar valued function f(x,y), the set of roots in general will be a curve. You can poke around randomly in the domain of interest until you find two points with function values of opposite sign, then apply the scalar bisection method to the segment between these points to find the intersection with the zero curve. – Lutz Lehmann Aug 20 '22 at 08:11
  • Take a look at the answers in this [question](https://stackoverflow.com/questions/3513660/multivariate-bisection-method), they might help. – AlberNovo Aug 20 '22 at 12:58
  • see my comment [here](https://stackoverflow.com/questions/36163846/how-approximation-search-works/36368290#comment114048508_36368290) and the next ones. also check out the answer above it. :) – Will Ness Oct 12 '22 at 08:21

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