Exam_3_Solutions

# Exam_3_Solutions - Name INTRODUCTION TO NUMERICAL METHODS...

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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 in-class 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 zero-tolerance 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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Name: ______________________________ 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 non-iterative 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 re-solve 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 ill-conditioned. 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 Gauss-Jordan 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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Exam_3_Solutions - Name INTRODUCTION TO NUMERICAL METHODS...

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