Let f RR be continuous. Which of the following statements about the bisection, secant, and Newton methods is/are correct?If f(a) < 0 and f(b) > 0, the error of the bisection method starting from [a, b] decreases exponentially with the number of iterations.For a starting interval [a, b], the bisection method fails if f(a) > f(b).If initialized sufficiently close to a simple root of a smooth (infinitely differentiable) function, the order of convergence of the secant method is approximately1.618.The secant method cannot be applied with a starting interval [a, b] such that f(a) = f(b).The order of convergence of the Newton method is 1.If f is smooth (infinitely differentiable) on the starting interval [a, b] and contains exactly one root x Є [a, b], then the bisection method will converge to thisroot.If f contains exactly one root in the starting interval [a, b] with ƒ(a)f (b) < 0, then the secant method will converge to this root.

Step 1:Step 2:Step 3: Step 4: Hence the Final answer is Hope this will clear your doubt. Please…

Answered: Let f RR be continuous. Which of the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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write a computer program that uses newtons method to find the root of a given function. and apply this program to find the root of the followig functions, using X0 as given . stop the iteration when the error as estimated by |Xn+1- Xn| is less than 10-6 . compare to your result for bisection.(a) f(x)=1-2xe-×/2 , X0=0; (b) f(X)=5-x-1, x0=1/4; (c) f(x)=x3-2x-5, x0=2; (d) f(x)=ex-2, x0=1; (e) f(x)=x-ex, x0=1; (f) f(x)=x6 - x -1, x0=1; (g) f(x)=x2 -sin x, x0=1/2; (h) f(x)=x3 - 2, x0=1; (i) f(x)=x+ tan x, x0=3; (j) f(x)=2 - x-1lnx , x0=1/3;
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