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

Economics, A mortgage lender seeks to maximize the expected value of its po...

A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the sum of all of the mortgages in it, so no generality is lost by examining t

Geometry, Determine the coordinates of the point equidistant from Salt Lake...

Determine the coordinates of the point equidistant from Salt Lake City and Helena

Theorem, #question if two angles of a triangle are unequal in measure then ...

#question if two angles of a triangle are unequal in measure then the side opposite to greater angle is longer than the side opposite to the smaller angle

Determine the transfer function, A digital filter has zero at z=a and poles...

A digital filter has zero at z=a and poles at z=b andz=c, where a, b, c are the real constants. Determine the transfer function and the frequency response function of the filter an

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

Partial Differentiation, If the sides angles of a triangle ABC vary in such...

If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0

Innovation, In the innovations algorithm, show that for each n = 2, the inn...

In the innovations algorithm, show that for each n = 2, the innovation Xn - ˆXn is uncorrelated with X1, . . . , Xn-1. Conclude that Xn - ˆXn is uncorrelated with the innovations X

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