Lecture 8 : Fixed Point Iteration Method, Newton’s Method
Theorem 8.1: Let g: [a;b]! [a;b] be a difierentiable function such that j g0(x) j • fi < 1 for all x 2 [a;b]: (4) Then g has exactly one flxed point l0 in [a;b] and the sequence (xn) deflned by the process (3), with a starting point x0 2 [a;b], converges to l0. Proof (*): By the intermediate value property g has a flxed point, say l0 ...
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