State the fixed point theorem giving the conditions that guarantee the iteration scheme x(n+1) = g(xn) is stable and has a unique fixed point in the interval [a, b]. Show that g(x) satisfies the conditions of this theorem in a neighbourhood of x∗.
State the fixed point theorem giving the conditions that guarantee the iteration scheme x(n+1) = g(xn) is stable and has a unique fixed point in the interval [a, b]. Show that g(x) satisfies the conditions of this theorem in a neighbourhood of x∗.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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State the fixed point theorem giving the conditions that guarantee the iteration
scheme x(n+1) = g(xn) is stable and has a unique fixed point in the interval [a, b].
Show that g(x) satisfies the conditions of this theorem in a neighbourhood of x∗.
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