COT4501
Fall 2010
Homework 1 solutions
1.3: Since the relative error = approximate valuetrue value , we get r = at from which we obtain that a =
true value
t
t(1 + r).
1.4: We have an error in the function value due to a perturbation h in the argument x.
COT4501 Spring 2012
Homework V
This assignment has seven problems. The assignment is due in class on Thursday, March
29, 2012. There are seven regular problems and two computer problems (using MATLAB).
For written problems, you need to show your work and
COT4501 Spring 2012
Homework II
This assignment has eight problems and they are equally weighted. The assignment
is due in class on Tuesday, February 14, 2012. There are six regular problems and two
computer problems (using MATLAB). For the computer probl
COT4501 Spring 2012
Homework IV
This assignment has seven problems. The assignment is due in class on Thursday, March
1, 2012. There are ve regular problems and two computer problems (using MATLAB). For
written problems, you need to show your work and it
COT4501 Spring 2012
Homework II Solutions
This assignment has eight problems and they are equally weighted. The assignment
is due in class on Tuesday, Tuesday 14, 2012. There are six regular problems and two
computer problems (using MATLAB). For the compu
COT4501 Spring 2012
Homework I
This assignment has seven problems and they are equally weighted. The assignment is
due in class on Tuesday, January 31, 2012.
Problem 1 Provide short answers to the following questions:
True or false: Floating-point number
Review Problems for Final Exam
Problem 1 Polynomial Interpolation
Given three data points (1, 2), (0, 1) and (1, 2)1 .
1. Let p(t) be the unique polynomial of degree n that interpolates the three data points
above. What is n?
2. Find p(t) using Lagrange i
COT4501 Spring 2012
Homework V
This assignment has seven problems. The assignment is due in class on Thursday, March
29, 2012. There are seven regular problems and two computer problems (using MATLAB).
For written problems, you need to show your work and
COT4501 Spring 2012
Homework VI
This assignment has seven problems. The assignment is due in class on Tuesday, April 10,
2012. There are seven regular problems and two computer problems (using MATLAB). For
written problems, you need to show your work and
COT4501 Spring 2012
Homework VII
The assignment is due in class on Thursday, April 19, 2012. There are ve regular problems and one computer problem (using MATLAB). For written problems, you need to show
your work and it is insufcient to just give the resu
Review Problems for Final Exam
Problem 1 Polynomial Interpolation
Given three data points (1, 2), (0, 1) and (1, 2)1 .
1. Let p(t) be the unique polynomial of degree n that interpolates the three data points
above. What is n?
2. Find p(t) using Lagrange i
COT4501 Spring 2012
Solution I
Problem 1 Provide short answers to the following questions:
1.8 False
1,10 False
1.23
1. No. Propagated data error is measured by the conditioning of an algorithm
and is not directly tied to stability.
2. Yes. Accuracy is
COT4501 Spring 2012
Homework III
This assignment has six problems and they are equally weighted. The assignment is due in
class on Tuesday, February 21, 2012. There are four regular problems and two computer problems (using MATLAB). For the computer probl
COT4501 Spring 2012
Solution I
Problem 1 Provide short answers to the following questions:
1.8 False
1,10 False
1.23
1. No. Propagated data error is measured by the conditioning of an algorithm
and is not directly tied to stability.
2. Yes. Accuracy is
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COT4501 Spring 2012
Homework III
This assignment has six problems and they are equally weighted. The assignment is due in
class on Tuesday, February 21, 2012. There are four regular problems and two computer problems (using MATLAB). For the computer probl
COT4501 Spring 2012
Homework IV Solutions
Problem 1
1. FALSE. for example following matrix has only one real eigenvalue.
2 1 1
A = 1 1 1 ,
11 2
2. False
3. For a given matrix
True
False
4. Which of the following conditions necessarily imply that a n n r
COT4501 Spring 2012
Homework V
This assignment has seven problems. The assignment is due in class on Thursday, March
29, 2012. There are seven regular problems and two computer problems (using MATLAB).
For written problems, you need to show your work and
Review Questions for Midterm Exam
1. Know the oating-point number systems. All problems in the four homework sets we have
had so far are fair questions to ask on the exam. The exam will cover the three chapters
we have covered so far: oating-point number
Scientic Computing
Approximations
Computer Arithmetic
Scientic Computing: An Introductory Survey
Chapter 1 Scientic Computing
Prof. Michael T. Heath
Department of Computer Science
University of Illinois at Urbana-Champaign
Copyright c 2002. Reproduction p
COT4501 Spring 2012
Homework II Solutions
This assignment has eight problems and they are equally weighted. The assignment
is due in class on Tuesday, Tuesday 14, 2012. There are six regular problems and two
computer problems (using MATLAB). For the compu
COT4501 Spring 2012
Homework VI
This assignment has seven problems. The assignment is due in class on Tuesday, April 10,
2012. There are seven regular problems and two computer problems (using MATLAB). For
written problems, you need to show your work and
COT4501 Spring 2012
Homework VII
The assignment is due in class on Thursday, April 19, 2012. There are ve regular problems and one computer problem (using MATLAB). For written problems, you need to show
your work and it is insufcient to just give the resu