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

Division of complex number, Division of complex number Now, we gave thi...

Division of complex number Now, we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so let's look at a couple of e

Distribution of sample distribution or sampling means , Distribution of Sam...

Distribution of Sample distribution or Sampling means A sample of size n is taken from the parent population and mean of the sample is estimated. It is repeated for a number o

Find the are length and sketch the level curves, 1) Find the are length of ...

1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2

1, how do you find the perimeter of an equalateral triangle

how do you find the perimeter of an equalateral triangle

Construct the adjacency matrix and the adjacency lists, Question: Constrcut...

Question: Constrcut the adjacency matrix and the adjacency lists for the graph G below, where the weights associated with edges represent distances between nodes. If no edge is pre

Decision-making under conditions of risk, Decision-making Under Conditions ...

Decision-making Under Conditions of Risk With decision-making under conditions of risk all possible states of nature are known and the decision maker has sufficient knowledge

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Find the probability distribution of x, If a pair of dice is thrown and X d...

If a pair of dice is thrown and X denotes the sum of the numbers on them. Find the probability distribution of X.Also find the expectation of X.     SOLUTION:    In a singl

Example on discrete mathematics, Suppose that at some future time every tel...

Suppose that at some future time every telephone in the world is assigned a number that contains a country code, 1 to 3 digits long, that is, of the form X, XX , XXX or followed

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