Nonlinear Equations : Esimating Roots by Newton's Method and Rate of Convergence
Not what you're looking for?
Please see the attached file for the fully formatted problem.
19. Show that x = tan^-1(x) has a solution alpha. Find an interval [a,b] containing alphasuch ythat for every x E [a,b] the iteration xn+1 = 1 + tan^-1(xn) n>=0 will converge to alpha. Calculate the first few iterates and estimate the rate of convergence.
Purchase this Solution
Solution Summary
Newton's Method is used to estimate a root and the rate of convergence is found. The solution is detailed and well presented. The solution was given a rating of "5" by the student who originally posted the question.
Solution Preview
Hello and thank you for posting your question to Brainmass!
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
Examine the function
And its graph:
This function is a continuous function, since it is the sum of continuous functions.
Now,
And
Thus there exist at least one ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.