CHEN 3201 Lecture Notes - Lecture 19: Rate Of Convergence, Taylor Series
28 Feb 2015
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Question 1: write down the form of the iterative scheme when you"re @ root for fixed point, by definition, for the left hand side of the eqn, ek+1 = error @ step k+1 multiply the right side side. Fundamental theorem of calculus there must exist some other point psi such that this is on the exam f --> g. Chen3201_numericalmethods page 1 a --> x* where really care about. 3 cases: , converges monotonically, | , oscillates but converges we"re ok with our method doing 1 or 2, but not with it doing 3. -> converges b/c f(x*) = 0 profided that f" does not go to 0 quickly we try to find if the function or its derivative gets small faster: picard"s method: this puts restriction on functions you can define. => only works for roots where this condition is true.
