436-536W06HW2 - MATH 436/536 HW 2 Due Wed February 22nd 1...

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MATH 436/536 - HW 2 Due Wed February 22 nd . 1) Use the Newton-Raphson method to find all 4 of the roots of the function I x x I x x I x f 5 4 7 ) 2 ( ) ( 2 3 4 + + - + - = to at least 15 digit accuracy. 2) For one of the complex roots in problem 1, show that the Newton-Raphson method has order of convergence which is 2, that is, in general each iteration of the method doubles the number of digits of accuracy over the previous iteration. 3) Plot all 4 Basins of Attraction with their Julia set (use at least 6 back iterations) for the function I x x I x x I x f 5 4 7 ) 2 ( ) ( 2 3 4 + + - + - = . 4) Use the two variable system version of the Newton-Raphson method to solve the system 36 ) 9 ( ) 7 ( 2 2 = - + + y x and 49 ) 10 ( ) 5 ( 2 2 = - + + y x for all 4 solutions. Now plot their 4 Basins of Attraction. 5) Use the Bisection method to find all of the real solutions of the equation 5 . 1 ) sin( 2 3 + = x e x accurate to at least 15 decimal places. 6) Is it possible to construct a version of the Bisection method for solving a system of two equations f(x, y) = 0 and g(x, y) = 0 for a real solution ( 29 0 0 , y x ?
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