# Numerical Analysis
Fall 2024

## Homework Assignments

Homework 1: Due Friday, September 6

1. Burden, Faires & Burden, Section 1.1: #10

2. Burden, Faires & Burden, Section 1.2: #2c, 4a, 5a (i,iii, iv(iii))

3. (a) Find two distinct 3-decimal digit floats in [1,100],
say a and b, with a less than b, so that fl( fl(a+b)/2 ) is not
in the interval [a,b].

(b) Now with these values of a and b, find fl( a + fl( fl(b-a)/2 ) ).

4. Let x be a (normal) float such that x+x overflows. What values can
fl(x+x-x-x) take, depending on the order of operations?

Homework 2: Due Friday, September 20

1. Burden, Faires, Section 2.1: #3c

2. Burden, Faires & Burden, Section 2.3: #1, 3a, 13bc (feel free to write code to help with 13, but do 1 and 3a by hand)

3. Burden, Faires & Burden, Section 2.4: #6, for MATH 53803 students, also do 2.4 #7a

4. Let f(x) = x^3 - 4.999x^2 + 6.996x - 2.997. Find the absolute
condition number for the problem "find the root of f nearest x = 1.01".

Homework 3: Due Friday, October 11

Burden, Faires & Burden, Section 3.1: #1b, 3b, 21, 17
(Hint for 17: see Example 4 in section 3.1)

Burden, Faires & Burden, Section 3.5: #13