Purchase Solution

# The answer to Fixed-point iteration

Not what you're looking for?

If the fixed-point iteration is applied to the function F(x) = 2 + (x-2)^4, starting at x = 2.5, what order of convergence results? Find the range of starting values for which this fixed-point iteration converges. Note that 2 is a fixed point.

Please provide as much detail as possible so that I can understand how the solution is derived. I would like to understand this problem so that I can apply the techniques used to similar problems. I really appreciate your help!

##### Solution Summary

Fixed-point iterations are analyzed.

##### Solution Preview

Assume that is the root of the fixed point equation
(1.1)
In addition is continuously differentiable for all x near  and for some .
Furthermore, assume that
(1.2)
Then if the initial guess is sufficiently close to , the iteration
(1.3)
Will ...

##### 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.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts