Consider the Fixed Point iteration algorithm defined by the formula za+1 = 9(In), where g(z) = I- a+ 2ae. Here a eR is a parameter. (a) Find the fixed point, p. (b) Does there exist a value of a for which the iterations could converge quadratically? If yes, find it and explain your answer.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 2CEXP
icon
Related questions
Question
Consider the Fixed Point iteration algorithm defined by the formula za+1 = 9(In), where g(z) =
I- a+ 2ae. Here a eR is a parameter.
(a) Find the fixed point, p.
(b) Does there exist a value of a for which the iterations could converge quadratically? If yes, find
it and explain your answer.
Transcribed Image Text:Consider the Fixed Point iteration algorithm defined by the formula za+1 = 9(In), where g(z) = I- a+ 2ae. Here a eR is a parameter. (a) Find the fixed point, p. (b) Does there exist a value of a for which the iterations could converge quadratically? If yes, find it and explain your answer.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Complexity
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage