CS 514/ Math 514 Numerical Analysis
Spring 2015
Homework 1
Given: Jan. 20, 2015; Due: Jan. 27, 2015 1:15 P.M. (15 minutes before class)
I would like you to work on Homework problems on your own without help from other students. If you are stuck on a probl
CS 514, Midterm solution
Problem 1 (20 pts, 2 pts each). (a) True. For example, (1 + (/2 +
/2) = 1 + while (1 + /2) + /2) = 1.
(b) False. Consider a base2 oating point system of largest exponent e
that is greater than the mantissa t. Consider x = 1.0 0 2
CS/MA51400 Homework4 Solution
March 18, 2015
1. Problem1 Given x1 = 1 and x2 = 2, we can get y1 = f (x1 ) = 1 and
y2 = f (x2 ) = 1 . Based on these two points, we can get the linear inter2
3
polation function p(x) = 1 x + 2 .
2
1
As f (x) = x , we can get
CS/MA51400 Homework4 Solution
April 29, 2015
1. Problem1
(a) After run the matlab code:
format long
h=zeros(1,14);
result=zeros(1,14);
h(1)=0.1;
for i=2:1:14
h(i)=(0.1)^i;
end
for i=1:1:14
result(i)=(exp(h(i)exp(h(i)/(2*h(i);
end
result
The results:
exp
CS 514/ Math 514 Numerical Analysis
Spring 2015
Problem Set 7
Given: April 23, 2015; NOT DUE. Use these problems to study for the Final Exam.
1. Sec 16.9, Problem 3.
2. Sec 16.9, Problem 6 (a).
3. Sec 16.9, Problem 6 (b).
4. Solve the difference equation
CS 514 HW 5 Solution
Problem 1. (a) To construct a C 1 piecewise quadratic interpolation of
the given values, we impose the following constraints
si (ti ) = f (ti )
(1)
si (ti+1 ) = f (ti+1 )
(2)
si (ti ) = si1 (ti )
i>0
(3)
s0 (ti ) = f (a)
(4)
for i = 0
CS 514/ Math 514 Numerical Analysis
Spring 2015
Homework 6
Given: April 14, 2015; Due: April 28, 2015 1:15 P.M. (15 minutes before class)
I would like you to work on Homework problems on your own without help from other students. If you are stuck on a pro
CS 514/ Math 514 Numerical Analysis
Spring 2015
Homework 5
Given: March 31, 2015; Due: April 14, 2015 1:15 P.M. (15 minutes before class)
I would like you to work on Homework problems on your own without help from other students. If you are stuck on a pro
CS 514/ Math 514 Numerical Analysis
Spring 2015
Homework 4
Given: Feb 27, 2015; Due: March 12, 2015 1:15 P.M. (15 minutes before class)
I would like you to work on Homework problems on your own without help from other students. If you are stuck on a probl
CS 514, HW3 solution
Problem 1. (25 pts) (a) [10 pts] Start with the expression xk+1 = xk
f
(xk )/ (xk ), substitute in the denition of (x) = f (x) and we get the ex(x)
pression asked to nd:
(x)
xk+1
[f (x)]2 f (x)f (x)
[f (x)]2
f (xk )f (xk )
= xk
.
[
CS 514/ Math 514 Numerical Analysis
Spring 2015
Homework 3
Given: Feb 12, 2015; Due: Feb. 26, 2015 1:15 P.M. (15 minutes before class)
I would like you to work on Homework problems on your own without help from other students. If you are stuck on a proble
CS/MA51400 Homework2 Solution
February 25, 2015
1. Problem1
n1
(a) Kf (x) = xnx
xn
related to x.
(b) Kf (x) = xe
ex
will be large.
x

=
xn
x
= n. So the condition number is not
= x. So when x inf, then condition number
x 1 
x
(c) Kf (x)
CS 514/ Math 514 Numerical Analysis
Spring 2015
Homework 2
Given: Jan. 29, 2015; Due: Feb. 12, 2015 1:15 P.M. (15 minutes before class)
I would like you to work on Homework problems on your own without help from other students. If you are stuck on a probl