Description of the assignment: find the solutions of the equation f(x)=-0.8x+20x²-10x-50 using the bisection and the Newton-Raphson methods seen in class. Discuss the performance, convergence properties, advantages and disadvantages of the two methods. Plot the curve and one of the solutions. Find the numerical values of all the solution using both methods. Steps and questions (all the underlined parts require an answer): 1) Select a proper range for the variable x and plot the function on that range. Question 1: Say how you selected the range and explain how many solutions do you expect to find. 2) Observing the plot, choose the initial interval or the initial points for the two algorithms. 3) Find the first solution, and then repeat the procedure until you find all the solutions, choosing different initial points or initial intervals, until all the solutions are found. List the numerical value of all of your solutions, and plot one of them on the curve. 4) For one of the solution, and for both methods, select different stopping parameters, and list the number of iterations needed to reach convergence, filling up the table below. Question 2: Comment your results and identify advantages and disadvantages of the two algorithms. Question 3: What does it happen if you do not put a stopping criterion and let the loop of the algorithms run for 1000 steps? Number of iterations Methods Bisection Newton-Raphson 10-3 10 10 10-12 5) Solve f(x)=0 with the Newton-Raphson method using different initial values x(1). In particular, try the initial values x(1)=-3.7 x(1)=-3.6 x(1)-3.1 and comment what you observe. Question 4: Does the Newton-Raphson algorithm always identify the solution that is closest to the initial point x(1)? Explain why.
Description of the assignment: find the solutions of the equation f(x)=-0.8x+20x²-10x-50 using the bisection and the Newton-Raphson methods seen in class. Discuss the performance, convergence properties, advantages and disadvantages of the two methods. Plot the curve and one of the solutions. Find the numerical values of all the solution using both methods. Steps and questions (all the underlined parts require an answer): 1) Select a proper range for the variable x and plot the function on that range. Question 1: Say how you selected the range and explain how many solutions do you expect to find. 2) Observing the plot, choose the initial interval or the initial points for the two algorithms. 3) Find the first solution, and then repeat the procedure until you find all the solutions, choosing different initial points or initial intervals, until all the solutions are found. List the numerical value of all of your solutions, and plot one of them on the curve. 4) For one of the solution, and for both methods, select different stopping parameters, and list the number of iterations needed to reach convergence, filling up the table below. Question 2: Comment your results and identify advantages and disadvantages of the two algorithms. Question 3: What does it happen if you do not put a stopping criterion and let the loop of the algorithms run for 1000 steps? Number of iterations Methods Bisection Newton-Raphson 10-3 10 10 10-12 5) Solve f(x)=0 with the Newton-Raphson method using different initial values x(1). In particular, try the initial values x(1)=-3.7 x(1)=-3.6 x(1)-3.1 and comment what you observe. Question 4: Does the Newton-Raphson algorithm always identify the solution that is closest to the initial point x(1)? Explain why.
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter29: Dc Generators
Section: Chapter Questions
Problem 5RQ: What are interpoles, and what is their purpose?
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Transcribed Image Text:Description of the assignment: find the solutions of the equation
f(x)=-0.8x+20x²-10x-50
using the bisection and the Newton-Raphson methods seen in class. Discuss the performance,
convergence properties, advantages and disadvantages of the two methods. Plot the curve and one of
the solutions. Find the numerical values of all the solution using both methods.
Steps and questions (all the underlined parts require an answer):
1) Select a proper range for the variable x and plot the function on that range.
Question 1: Say how you selected the range and explain how many solutions do you expect to
find.
2) Observing the plot, choose the initial interval or the initial points for the two algorithms.
3) Find the first solution, and then repeat the procedure until you find all the solutions, choosing
different initial points or initial intervals, until all the solutions are found. List the numerical value
of all of your solutions, and plot one of them on the curve.
4) For one of the solution, and for both methods, select different stopping parameters, and list the
number of iterations needed to reach convergence, filling up the table below.
Question 2: Comment your results and identify advantages and disadvantages of the two
algorithms.
Question 3: What does it happen if you do not put a stopping criterion and let the loop of the
algorithms run for 1000 steps?
Number of iterations
Methods Bisection
Newton-Raphson
10-3
10
10
10-12
5) Solve f(x)=0 with the Newton-Raphson method using different initial values x(1). In particular,
try the initial values
x(1)=-3.7
x(1)=-3.6
x(1)-3.1
and comment what you observe.
Question 4: Does the Newton-Raphson algorithm always identify the solution that is closest to the
initial point x(1)? Explain why.
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