Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 1
Assigned: Monday, January 3, 2011.
Due: Friday, January 14, 2011.
Include a cover page and a problem sheet.
Always clearly label all plots (title, x-label, y-label, and legend).
Use
Math 371 - Introduction to Numerical Methods - Winter 2009
Homework 3
Assigned: Wednesday, February 2, 2011.
Due: Friday, February 11, 2011 at 2 PM.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicat
Rate of Convergence
Sequence 1. This computes a sequence xn that converges to 2. This sequence has a rate of convergence O 1 n3 . A possible
value of 5. Looking at the table below we can see that indeed, the error xn
x n_
n_
x 5;
2 n^3 1
1 n^3 ;
Grid Ta
Newton vs. Secant Method
Newton's Method
First we define a function f(x) and ask Mathematica to find a root of this function close to 1.
f x_
Exp x
x
4
root
x
x^2
x
4
x2
x
FindRoot f x ,
x, .5
1.28867796682387
act
x . root
1.28867796682387
For Newton's Me
Chebyshev Nodes
Definitions and Basics
In this notebook I will do an example where the nodes of an interpolating polynomial are determined by using the zeros of a Chebyshev Polynomial.
The Chebyshev Polynomials are defined for x in the interval [-1, 1] an
Cubic Spline
Suppose we are given a set of interpolating points (xi , yi ) for i = 0, 1, 2, 3 . . . n. We
seek to construct a piecewise cubic function s(x) that has the for x [xj , xj+1 ] we have:
s(x) = sj (x) = aj + bj (x xj ) + cj (x xj )2 + dj (x xj )
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 4
Assigned: Friday, February 11, 2011.
Due: Monday, February 28, 2011 at 2 PM.
1. In this problem we will investigate the Cubic Spline problem and compare the
convergence using dierent bo
Accelerating Convergence
Suppose we have a fixed point method that converges linearly. Then we talked about
the fact that:
en
p
g' p
1 g' p
pn
pn
pn
1
and
g' p
pn pn 1
pn 1 pn 2
So, if we put these two expressions together we have that
p
pn pn 1 2
pn pn 2
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 2
Assigned: Friday, January 14, 2011.
Due: Thursday, January 27, 2011.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicate clearly
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 5
Assigned: Friday, February 28, 2011.
Due: Monday, March, 14, 2011 at 2 PM.
All normal rules apply
1. Section 3.1 #3 Do this by hand and show your work clearly.
Solve the following syste
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 4
Assigned: Friday, February 11, 2011.
Due: Monday, February 28, 2011 at 2 PM.
All normal rules apply
1. In this problem we will investigate the Cubic Spline problem and compare the
conve
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 5
Assigned: Friday, February 28, 2011.
Due: Monday, March, 14, 2011 at 2 PM.
All normal rules apply
1. Section 3.1 #3 Do this by hand and show your work clearly.
2. Section 3.2 # 4 Do thi
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 2
Assigned: Friday, January 14, 2011.
Due: Thursday, January 27, 2011 at 2PM.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicate c
Math 371 - Introduction to Numerical Methods - Winter 2009
Homework 3
Assigned: Wednesday, February 2, 2011.
Due: Friday, February 11, 2011 at 2 PM.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicat
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 1
Assigned: Monday, January 3, 2011.
Due: Friday, January 14, 2011.
Include a cover page and a problem sheet.
Always clearly label all plots (title, x-label, y-label, and legend).
Use