# hw _4 - 650:231 M.E Computational Analysis and Design...

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650:231 M.E. Computational Analysis and Design Homework #4: Finding the Roots of f(x) 1 . [6 pts.] Fixed point Iteration for Two obvious candidates for fixed-point iteration functions are , and . (a) First, plot for 0<x<30. Verify that f(x)=0 has two roots: one near x=1.5 and another near x=21. All of the above three iteration formulas converge to these roots given reasonable initial guess. Demonstrate graphically the solution procedure of the successive substitution method following the instruction below: (b) Rearrange the above equation to the form and plot the curve and y=x for 0<x<30. (c) Illustrate the iteration procedure in the fixed-point iteration method starting at x=20. The plot for the curves y= and y=x with the initial guess of x=20 looks like Fig 1. Fig 1. Does this converge? If so, to which value does this converge? (d) Based on program my_fixpt of LA#4_Pr#1, write a MATLAB function m-file for the fixed-point iteration using , whereis the generic function to be used in the fixed point iteration such as above. In the program include: 1) Plot of y=x and

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650:231 M.E. Computational Analysis and Design 2) Plot of a sequence of vertical line (, 0) to (, horizontal line to , , where vertical line , to , horizontal line , to ,, where using dotted lines as in Figures 2.4 and 2.5 of LA #4_Pr#1.
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