Math 5334: Homework 1 Solutions
Victoria E. Howle
February 6, 2008
Problem 1.33
For each value of the exponent e, we have 2t possible oating point numbers,
where t is the number of bits used by the mantissa f in a oating point
number (1 + f ) 2e . For exa
Math 5334: Homework 1 Solutions
February 3, 2009
Problem 1.33
For each value of the exponent e, we have 2t possible oating point numbers, where t is the number of bits used
by the mantissa f in a oating point number (1 + f ) 2e . For example, if t = 3, fo
Math 5334: Homework 2 Solutions
Victoria E. Howle
February 20, 2008
Problem 2.15
a. The condition number of golub(n) grows exponentially.
x = [];
y = [];
% For golub matrices size n = 1 to 10, we will run 10 tests of
% the condition number for each size n
Math 5334: Homework 2 Solutions
February 14, 2009
Problem 2.3
For this problem, we rewrite the 13 equations (and 13 unknowns) as a linear system F f = b and
solve for f with f = F \b. The script prob2 3.m builds F and b and solves for f.
Problem 2.5
a. If
Math 5334: Homework 3 Solutions
Victoria E. Howle
March 31, 2008
Problem 4.3
a. Since I dont see any easy roots (0 or 1) of
p(x) = 816x3 3835x2 + 6000x 3125
I will nd them with MATLAB:
> format long
> roots([816 -3835 6000 -3125])
ans =
1.666666666666808
Math 5334: Homework 4 Solutions
Victoria E. Howle
April 8, 2008
Problem 6.1
Well just plug in each function to quadgui and have it report back the number of function evaluations (fcount). I am basing the areas where function
evaluations are concentrated f
Math 5334: Homework 4 Solutions
March 7, 2009
Problem 5.4
a. We have dened = 1/( uk ) and want to show that = 2/ u 2 . First we will look at u 2 :
2
u
= uu
= (x + ek ) ( + ek )
x
= x1 x1 + + (xk + )(k + ) + + xn xn
x
=
x
2
+ xk + xk +
xk xk
xk xk
xk xk
=
Math 5334: Homework 5 Solutions
April 29, 2009
Problem 6.6
The error function erf(x) is dened by
2
erf(x) =
x
2
ex dx.
0
As in the previous problem, we will make an inline function for the integrand, then for this problem,
well use a script to run quadtx