Question 2 (a) [1, 2]. Use the Theorem from the course to prove that g(x) = 1+ e¬¤ has a unique fixed point on
Question 2 (a) [1, 2]. Use the Theorem from the course to prove that g(x) = 1+ e¬¤ has a unique fixed point on
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 17EQ
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Expert Solution
Step 1
For the given function has a unique fixed point on .
The theorem says that,
- is defined and differentiable on
- There is a number such that then there is a unique fixed point.
Since is defined and differentiable on
The values for the exponential function at x = 1, 2
both belongs to
Step 2
Now the derivative ,
Therefore, there exists a unique fixed point.
As satisfies all the criterion of the theorem therefore, converges.
Given that
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