Brouwer's Fixed Point Theorem (Proof)
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Brouwer's Fixed Point Theorem (Proof)
Today I'd like to talk about Brouwer's Fixed Point Theorem. Literally! It's the subject of this week's episode on PBS Infinite Series. Brouwer's Fixed Point Theorem is a result from topology that says no matter how you stretch, twist, morph, or deform a disc (so long as you don't tear it), there's always one point that ends up in its original ...
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SOLVED: Consider the following fixed-point iteration algorithm: Xi 1 = g(xi) = Xi 1. From a graphical solution of x = g(x), you know that X = 2.24 is approximately the fixed point of x = g(x).If you start the fixed-point algorithm with Xo = 2.4, how many iterations do you need to perform at least in order to reach an error less than 10^-7?Use your knowledge about the order of convergence of the fixed-point method to conduct your analysis.Answer:
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