Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 1
January 11, 2013
1. (10 points) Consider the oating point number system consisting of all numbers
.d1 d2 e , where = 3, 1 e 1, 0 < d1 < 3, and 0 d2 < 3. Write down in
rational form all of the positive numbers in this system. Wha
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 7
February 11, 2013
1. (10 points) Write a code implementing naive Gaussian elimination followed by back
substitution. You can obtain the algorithms from the Handouts link on the web pages.
The handout for the algorithms may seem
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 9
February 22, 2013
1. (10 points) Consider the following values of (ti , yi ), i = 1, . . . , 8:
(.2, .05446), (.3, .098426), (.6, .33277), (.9, .72660),
(1.1, 1.0972), (1.3, 1.5697), (1.4, 1.8487), (1.6, 2.5015).
a. Form the nor
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 8
February 19, 2013
1. (10 points) Consider the simple static system illustrated. This consists of 13 rigid
members connected at 8 joints, each of which allows free rotation. All horizontal and
vertical members are of length one;
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 6
February 1, 2013
p satises the xedpoint equation
1. a. (10 points) If p is any positive number, then x =
1
p
x = g (x) x +
.
2
2x
What can you say about the local convergence of xedpoint iterates to p ? (Do
they converge to p
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 2
January 15, 2013
1. (10 points) The sum
1 1/2 + 1/3 1/4 + . . . =
j =1
(1)(j 1)
j
is convergent (conditionally if not absolutely). Suppose we want to evaluate a partial
N
sum j =1 (1)(j 1) /j for some very large N . Since succes
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 3
January 18, 2012
1. (10 points) Suppose you apply the bisection method to determine an approximate solution
x of f (x) cos(x) ex + 1 = 0. Suppose the initial interval is [a, b] = [0, /2]. How many
iterations of the method are re
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 5
January 29, 2013
Use MATLABs fzero routine for the problems below. To see details of the iterations, set
options = optimset(display,iter)
and use either the form
fzero(fun,[a,b],options),
if your function is dened as an anonymou
Numerical Methods for Linear and Nonlinear Systems
MA 3257

Spring 2013
MA 3257/CS 4032
Homework 4
January 24, 2012
1. (30 points) Write codes for the bisection method, Newtons method, and the secant
method. Use them to solve the following problems.
a. Find the unique positive solution of cos(x) ex + 1 = 0.
b. Find the rst tw