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Using the Fixed-point iteration method, find the roots of the function: f(x) = x^4 - 20x^2 + x a). How many roots are expected? Can this problem be simplified before computing? b). For fixed point iteration, we need to resolve f(x) = 0 to the form g(x) = x. Find three functions that satisfy this form. c). Calculate derivative g'(x) for all three functions and determine the range in which Ig(x)| < 1 is met

Using the Fixed-point iteration method, find the roots of the function: f(x) = x^4 - 20x^2 + x a). How many roots are expected? Can this problem be simplified before computing? b). For fixed point iteration, we need to resolve f(x) = 0 to the form g(x) = x. Find three functions that satisfy this form. c). Calculate derivative g'(x) for all three functions and determine the range in which Ig(x)| < 1 is met

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using the Fixed-point iteration method, find the roots of the function: f(x) = x^4 - 20x^2 + x a). How many roots are expected? Can this problem be simplified before computing? b). For fixed point iteration, we need to resolve f(x) = 0 to the form g(x) = x. Find three functions that satisfy this form. c). Calculate derivative g'(x) for all three functions and determine the range in which g(x)| < 1 is met d). Plot the three functions and try to root graphically, starting with the initial value x = 3.
Transcribed Image Text:Using the Fixed-point iteration method, find the roots of the function: f(x) = x^4 - 20x^2 + x a). How many roots are expected? Can this problem be simplified before computing? b). For fixed point iteration, we need to resolve f(x) = 0 to the form g(x) = x. Find three functions that satisfy this form. c). Calculate derivative g'(x) for all three functions and determine the range in which g(x)| < 1 is met d). Plot the three functions and try to root graphically, starting with the initial value x = 3.
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