Numerical Analysis                Fall 2022

Homework Assignments


Homework 1: Due Friday, September 9

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

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

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

4. Let x be a 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 23

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

2. Burden, Faires & Burden, Section 2.3: #1, 3a, 13bc

3. Burden, Faires & Burden, Section 2.4: #6, for MATH 5383 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 14

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

Burden, Faires & Burden, Section 3.5: #13

Homework 4: Due Friday, October 28

1. Burden, Faires & Burden, Section 4.1: #6b

2. Burden, Faires & Burden, Section 4.3: #5d, 22

3. Burden, Faires & Burden, Section 4.4: #3f

Homework 5: Due Wednesday, December 7

1. Burden, Faires & Burden, Section 5.2, #1c

2. Burden, Faires & Burden, Section 5.3, #1c

3. Using the identity dy/dt = f(t,y), give an expression for d^2/dt^2 { f(t,y(t)) } (for arbitrary, but smooth f) in terms of f and its partial derivatives wrt t and y.

4. Burden, Faires & Burden, Section 5.4, #1c

5. Burden, Faires & Burden, Section 5.6, #1c (explicit 2-step only)