Bisection method and the newton method, Mathematics

Assignment Help:

1. Write two m-files, one for the bisection method and another for Newton's method.

2. Using both the Bisection method and the Newton method answer the following:

Include the commands you typed into Matlab

a) Find the root to 3, 5, and 8 decimal places of f(x) = x2- 2 starting with an initial approximation of x=1.

b) How many steps did it take for the bisection method to find the root to 3, 5, and 8 decimal places?

c) How many steps did it take for the Newton method to find the root to 3, 5 and 8 decimal places?

3. Use Newton's method to find all the real roots of f(x) = x5+ x4 -4x3 - 3x2- 3x +1

4. Apply Newton's method to the function f(x) = x3 - x with an initial approximation of x=1/√5.  Is the method converging?  What happens?  Explain your answer using the graph of f(x).

5. Use Newton's method on the function (x) = 3√5 . What happens when your initial approximation is not x=0?  Explain your answer using the graph of f(x).


Related Discussions:- Bisection method and the newton method

Wit tester., two fathers and two sons went fishing . they caught only 3 fis...

two fathers and two sons went fishing . they caught only 3 fish and divided them equally among themselves without cutting. is it possible? how?

Methods of sampling, a.      Random or probability sampling methods they in...

a.      Random or probability sampling methods they involve: Simple random sampling Systematic sampling Stratified sampling Multi stage sampling   b.

Calculate the area of rectangle , Calculate the area of RECTANGLE ? Th...

Calculate the area of RECTANGLE ? The area of a rectangle is the amount of space taken up by a rectangle, which is a two-dimensional shape. You find the area (A) of a recta

What is minimum spanning tree, What is minimum spanning tree?  Determine a ...

What is minimum spanning tree?  Determine a railway network of minimal cost for the cities in the following graph using Kruskal's algorithm. Ans: Minimum spanning tree in a con

Simultaneous equations, i need a step by step guide to answering simultaneo...

i need a step by step guide to answering simultaneous equation for gcses

#Famous Numbers Exercise, Euler''s Constant (e) Approximate the number to t...

Euler''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.

Area in polar cordinates, find the area of the region within the cardioid r...

find the area of the region within the cardioid r=1-cos

Piecewise, x=±4, if -2 = y =0 x=±2, if -2 = y = 0

x=±4, if -2 = y =0 x=±2, if -2 = y = 0

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd