08 - Lecture 8 Todays class: The method of false position...

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Unformatted text preview: Lecture 8 Todays class: The method of false position for finding zeros Fixed-point iteration The Newton-Raphson method The secant method Determining convergence of an iterative method Method of False Position Input : f , x ,x u with x < x u and f ( x ) f ( x u ) < n while not converged x n r x n u- f ( x n u ) ( x n - x n u ) f ( x n )- f ( x n u ) x n +1 ,x n +1 u ( [ x n , x n r ] , if f ( x n ) f ( x n r ) [ x n r ,x n u ] , otherwise n ( n + 1) Test for convergence end while Output : Final bracket [ x n ,x n u ] Example Apply the method of false position (using a calculator) to compute an estimated solution x 3 r of the cubic equation x 3 + 4 x 2 = 10 together with a bracket x 3 ,x 3 u . Start from the initial bracket x ,x u = [1 , 2].-1.602274384 1.26315789474 1.33882783883 1.00000000000 2.00000000000 1.26315789474 2.00000000000 1 2-0.430364748 2.00000000000 1.33882783883 1.35854634182-0.110008788 3 1.35854634182 2.00000000000 Fixed-point iteration...
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This note was uploaded on 06/20/2011 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Winter '10 term at UOIT.

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08 - Lecture 8 Todays class: The method of false position...

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