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In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that ƒ € C³[a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h+h²f"" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i² = −1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step.

In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that ƒ € C³[a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h+h²f"" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i² = −1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Could you please do the Python coding with the correct indentations and answer for question 5a, 5b, 5c?  The questions are in the image. 

5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that fe C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h + h²f" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i2= -1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step. f(xk) Im(f(xk+ih)) Tk+1=kh- k = 0, 1, 2,... with given ro. Modify your code with Newton's method of problem 4 so as the default value of the derivative df to be the new approximation Im(f(ro+ih))/h. Assume that |æk+1=x*| kx|kx* |r where 2* is such that f(r*) = 0. This means that the convergence rate of the new method is r. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Study the influence of the parameter h in the convergence rate. lim = C > 0,
Transcribed Image Text:5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that fe C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h + h²f" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i2= -1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step. f(xk) Im(f(xk+ih)) Tk+1=kh- k = 0, 1, 2,... with given ro. Modify your code with Newton's method of problem 4 so as the default value of the derivative df to be the new approximation Im(f(ro+ih))/h. Assume that |æk+1=x*| kx|kx* |r where 2* is such that f(r*) = 0. This means that the convergence rate of the new method is r. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Study the influence of the parameter h in the convergence rate. lim = C > 0,
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Could you please clarify if the this is the Python coding with the correct indentations and answer for question 5a, 5b, 5c?  The questions are in the image. 

 
5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that fe C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h + h²f" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i2= -1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step. f(xk) Im(f(xk+ih)) Tk+1=kh- k = 0, 1, 2,... with given ro. Modify your code with Newton's method of problem 4 so as the default value of the derivative df to be the new approximation Im(f(ro+ih))/h. Assume that |æk+1=x*| kx|kx* |r where 2* is such that f(r*) = 0. This means that the convergence rate of the new method is r. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Study the influence of the parameter h in the convergence rate. lim = C > 0,
Transcribed Image Text:5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that fe C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h + h²f" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i2= -1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step. f(xk) Im(f(xk+ih)) Tk+1=kh- k = 0, 1, 2,... with given ro. Modify your code with Newton's method of problem 4 so as the default value of the derivative df to be the new approximation Im(f(ro+ih))/h. Assume that |æk+1=x*| kx|kx* |r where 2* is such that f(r*) = 0. This means that the convergence rate of the new method is r. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Study the influence of the parameter h in the convergence rate. lim = C > 0,
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