Math6643Fall2010ExamLatexWSolutions

Math6643Fall2010ExamLatexWSolutions - Math/CSE 6643 Exam...

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Unformatted text preview: Math/CSE 6643 Exam Fall 2010 Name: Put your name on all sheets now. 80 minutes, 8 questions for 80 points total. No calculators, electronic devices, books, or notes are permitted. Use a pen, put a box around your final answers, and cross out anything that is not to be graded. No credit is given for answers without the reasoning that leads to them: show all work . If you need more space, continue onto the back (and write that you have done so at the bottom of the front side). 1. (10 points) Find the rank-one matrix which is the best approximant to A = 2 1 0 1 in the matrix 2 norm. A * A = 2 0 1 1 2 1 0 1 = 4 2 2 2 . λ 2- 6 λ + 4 = 0 ,λ = 3 ± √ 5. A * A = V Σ 2 V * , σ 1 = p 3 + √ 5. v 1 in kernel of 1- √ 5 2 2- 1- √ 5 so v 1 = [1 + √ 5 , 2] T / p 10 + 2 √ 5. Av 1 = σ 1 u 1 . The best rank-1 approximation is σ 1 u 1 v T 1 = Av 1 v T 1 = 2 1 0 1 6 + 2 √ 5 2 + 2 √ 5 2 + 2 √ 5 4 1 10 + 2 √ 5 = 14 + 6 √ 5 8 + 4 √ 5 2 + 2 √ 5 4 1 10 + 2 √ 5 1 Math/CSE 6643 Exam Fall 2010...
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This note was uploaded on 12/25/2011 for the course MATH 6643 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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Math6643Fall2010ExamLatexWSolutions - Math/CSE 6643 Exam...

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