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

Dilemmas of america''s minority groups, Explain this statement " As we begi...

Explain this statement " As we begin the 21st century, the dilemmas of America's minority groups remain perhaps the primary unresolved domestic issue facing the nation." How might

Calculate the probability, Given the following decision tree, perform the t...

Given the following decision tree, perform the tasks listed below  1. Simulate the route through the test market and produce results for twenty simulations, calculating the

Find out the absolute extrema for function and interval, Find out the absol...

Find out the absolute extrema for the given function and interval.  g (t ) = 2t 3 + 3t 2 -12t + 4 on [-4, 2] Solution : All we actually need to do here is follow the pr

Calculate probability, The following table contains some information about...

The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable

Characteristics of time series, Characteristics of Time Series Time se...

Characteristics of Time Series Time series has the given characteristics. a) A long term trend (T) -tendency of the whole series to fall and rise. b) Seasonal variati

Factorization of expressions, Above we have seen that (2x 2 - x + 3)...

Above we have seen that (2x 2 - x + 3) and (3x 3 + x 2 - 2x - 5) are the factors of 6x 5 - x 4 + 4x 3 - 5x 2 - x - 15. In this case we are able to find one facto

Example of subtraction of fractions, Example of Subtraction of Fractions: ...

Example of Subtraction of Fractions: 1/3 + 1/6 + 1/8 = ____ Using trial & error we could search that 24 is the LCD or smallest number in which 3, 6, and 8 will all divide w

the bug should start to move in order to increase, The temperature at the ...

The temperature at the point (x, y) on a metal plate is given by the function f(x, y) = x 3 + 4xy + y 2 where f is in degrees Fahrenheit and x and y are in inches, with the origin

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