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Name: ______________________________
Spring 2008
1
INTRODUCTION TO NUMERICAL METHODS OF ENGINEERING ANALYSIS
EGM 4344
EXAM 3
General instructions:
This exam is closed book and closed notes except for one page, front and
back. The only allowable calculator functions for the inclass portion are +, , *, /, sin, cos, and ^,
and sqrt.
All work on this exam should be done individually, and you are reminded that the University of
Florida has an honor code.
The instructor has a zerotolerance policy for cheating on exams. Any suspected violation of the
honor code will be reported to Student Judicial Affairs. If you are found guilty, you may receive
a permanent mark on your UF academic transcript and will receive an automatic failing grade in
this course.
NO CREDIT WILL BE GIVEN FOR CORRECT ANSWERS WITHOUT SHOWING YOUR
WORK. Please show all your work clearly and neatly, as partial credit will be given
if
it is clear
that you understood the concepts required to solve the problem.
All three problems should be completed.
No credit will be given without a signature and date on
the honor code statement below
. Note that an extra credit problem is also provided worth 5
additional points.
I pledge my honor that I did not violate the University of Florida honor code during this
exam.
Signature:
Date:
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Spring 2008
2
Problem 1 – General Concepts.
(30 points)
Below are 30
brief
conceptual questions. Each question counts for 1 point, and no partial credit
will be given for incorrect or partially correct answers.
Linear Algebra
1. When are iterative methods preferred over noniterative methods for solving a system of linear
algebraic equations?
When the linear system possesses an extremely large number of unknowns.
2. Explain briefly why LU decomposition is useful.
It allows you to resolve Ax = b for different b vectors without having to refactor the A matrix.
3. What are the two steps involved in performing naïve Gaussian elimination (i.e., without partial
pivoting)?
1)
Forward elimination
2)
Back substitution
4. List two tests that you can use to determine if a linear system of equations is illconditioned.
1)
Determinant is “close” to zero
2)
Condition number is “large” (same as inverse condition number is “close” to zero)
5. What is the main reason why it is usually easier to solve a linear system of equations than it is
to solve a nonlinear system of equations?
Usually you don’t have to iterate when solving a linear system of equations, which also means
no initial guess (no iteration or no initial guess required are both acceptable answers).
6. What is the difference between an overdetermined and undertermined system of linear
equations?
Overdetermined has more equations than unknowns, underdetermined has fewer equations than
unknowns.
7. Given a linear system
b
Ax
=
where
A
is a symmetric positive definite matrix, rank the
following three solution methods for efficiency, with 1 being the most efficient (i.e., fewest
operations) and 3 being the least efficient:
2
Gassian Elimination Method
3
GaussJordan Method
1
Choleski Decomposition Method
Name: ______________________________
Spring 2008
3
8. The fixed point iteration root finding method can be used to solve a linear system of equations.
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.
 Spring '09
 RAPHAELHAFTKA

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