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Unformatted text preview: Foundations of Computational Math I Exam 1 Takehome Exam Open Notes, Textbook, Homework Solutions Only Calculators Allowed Tuesday 19 October, 2010 Question Points Points Possible Awarded 1. Basics 15 2. Bases and Orthogonality 20 3. Factorization 30 Complexity 4. Backward Stability 30 5. Conditioning and 25 Backward Error Total 120 Points Name: Alias: to be used when posting anonymous grade list. 1 Problem 1 (15 points) Each question below has a brief answer and justification. 1.a . (5 points) Explain the idea of a hidden bit in a floating point system with base = 2 and the benefit achieved by using it. 1.b . (5 points) Can the idea of a hidden bit be usefully generalized to a floating point system with base 6 = 2? 1.c . (5 points) Suppose you have a problem whose condition number is 10 5 . Given that you want at least 2 digits of accuracy in the solution how many decimal digits would you recommend be used in the floating point system used to solve the problem? 2 Problem 2 (20 points) Consider the vector space R 3 and the subspace S of dimension 1 given by S = span [ v 1 ] , v 1 = 1 1 1 2.a . Determine a basis....
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This note was uploaded on 07/25/2011 for the course MAD 5403 taught by Professor Gallivan during the Spring '11 term at University of Florida.
 Spring '11
 Gallivan

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