q = 4 Q2 Consider the equation x -3x'te0 (a) Write this equation as x =g(x) in three different forms. Apply convergence test to each of these forms. Which g(r) is more suitable for the fixed point...
q=4 Consider the equation x-3x4 +e (a) Write this equation as x -g(x) in three different forms. Apply convergence test to each of these forms. Which g(x) is more suitable for the fixed point iteration b) Compute first 4 iterations by takingx- and graph each value of x and g (x) to show convergence or divergence of the scheme. Find the fixed point of g(x) correct to 5 decimal digits using the following fixed- point iteration calculator. (c) https://planetcalc.com/2824/ Consider...
Use Matlab. Thanks! 2. For the equation et = x + 2, (a) use the fixed point iteration method to determine its two roots to eight correct decimal places (you may need to write this equation in two different ways of x = g(x) in order to obtain these two roots); (b) numerically calculate the convergence rates for your converged iterations; (c) compare these numerical convergence rates with the theoretical conver- gence rates we presented in class (also see Theorem...
2. (a) Suppose we have to find the root xof x); that is, we have to solve )0. Fixed-point methods do this by re-writing the equation in the form x·= g(x*) , and then using the iteration scheme : g(x) Show this converges (x-→x. as n→o) provided that K < 1 , for all x in some interval x"-a < x < x*+a ( a > 0 ) about the rootx 6 points] (b) Newton's method has the form of...
1. tain a rough estimate of all real roots of the function f(x) searching in [-2,2]. Use Ax1 ex-2 by incremental b) Obtain two iterating functions for finding each of these roots by fixed-point iteration by solving for each x which appears in the equation c) Without doing any iterations, determine if each iterating function will converge to each root and state whether the convergence or divergence will be monotonic or oscillatory d) From the iterating functions obtained in part...
a) Obtain a rough estimate of all real roots of the function f)ex x-2 by incremental searching in [-2,2]. Use Ax1 b) Ob tain two iterating functions for finding each of these roots by fixed-point iteration by solving for each χ which appears in the equation. Without doing any iterations, determine if each iterating function will converge to each root and state whether the convergence or divergence will be monotonic or oscillatory d) c) From the iterating functions obtained in...