Please do the following questions with the full python coding and explanation below each question typed
Please do the following questions with the full python coding and explanation below each question typed
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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Please do the following questions with the full python coding and explanation below each question typed
![4.
The following algorithm for approximating roots combines the bisection method with
Newton's method and ensures the convergence even in the case where Newton's method fail to
converge.
Choose an interval [a, b] such that f(a) f(b) ≤0.
Compute initial approximation ro= (a + b)/2 of the root using the bisection method.
For i=1,2,...
Computer using Newton's method and Ti-1.
If ri[a,b], set x₁ = (a+b)/2 (from bisection).
Check for convergence.
If f(a) f(xi) ≤0 set b = xi, else set a = x₁.
(a)
Implement this algorithm in a PYTHON function with the following specifications:
findzero (a, b, tol, maxit, f, df)
def
# Input:
# a, b = The endpoints of the interval
# tol = The required tolerance
# maxit = Maximum number of iterations
#f, df = The function and its derivative
# Output:
# star = approximation of root
#niter = number of iterations for convergence
#ierr =
#
#
#
0, the method converged
1, df was zero or undefined
2, maximum number of iterations has been reached
return xstar, niter,ierr
(b)
Use this function with input parameters of your choice to find approximations of the
roots of Problem 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2Fe4d18cba-c238-4a76-99c0-8c00b5456b1d%2Fu71hcb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.
The following algorithm for approximating roots combines the bisection method with
Newton's method and ensures the convergence even in the case where Newton's method fail to
converge.
Choose an interval [a, b] such that f(a) f(b) ≤0.
Compute initial approximation ro= (a + b)/2 of the root using the bisection method.
For i=1,2,...
Computer using Newton's method and Ti-1.
If ri[a,b], set x₁ = (a+b)/2 (from bisection).
Check for convergence.
If f(a) f(xi) ≤0 set b = xi, else set a = x₁.
(a)
Implement this algorithm in a PYTHON function with the following specifications:
findzero (a, b, tol, maxit, f, df)
def
# Input:
# a, b = The endpoints of the interval
# tol = The required tolerance
# maxit = Maximum number of iterations
#f, df = The function and its derivative
# Output:
# star = approximation of root
#niter = number of iterations for convergence
#ierr =
#
#
#
0, the method converged
1, df was zero or undefined
2, maximum number of iterations has been reached
return xstar, niter,ierr
(b)
Use this function with input parameters of your choice to find approximations of the
roots of Problem 3.
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