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Course: MATH 2601, Fall 2009
School: Georgia Tech
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Word Count: 190

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Homework Problems (Week 8) (Householder re ection, Givens rotation, Fixed point method) PROBLEM 1. Find the Householder re ection matrix that maps the vector 1 v = 2 4 into a vector Hv such that only its rst entry be nonzero. PROBLEM 2. (i) Find the QR 1 0 A= 1 factorization of 1 2 2 3 1 1 with Householder re ections. (ii) Find the QR factorization of 1 1 A = 0 2 1 2 with Householder re ections. PROBLEM 3. Let...

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Homework Problems (Week 8) (Householder re ection, Givens rotation, Fixed point method) PROBLEM 1. Find the Householder re ection matrix that maps the vector 1 v = 2 4 into a vector Hv such that only its rst entry be nonzero. PROBLEM 2. (i) Find the QR 1 0 A= 1 factorization of 1 2 2 3 1 1 with Householder re ections. (ii) Find the QR factorization of 1 1 A = 0 2 1 2 with Householder re ections. PROBLEM 3. Let again 1 1 A = 0 2 1 2 2 3 1 2 3 1 as above. Find the QR-factorization of A using Givens rotations. PROBLEM 4. (i) Find the solution to the equation x = ln(2 x) by a the two year old child naive iteration (Section 4.1) up to four decimals. (ii) Find the solution to the same equation with Newton s method. Which one is faster? (If you have forgotten, review Newton s method from Chapter 3.9, Salas-Hille-Etgen!) 1 PROBLEM 5. Try to nd the solution to 10 x3 = x by the two year old child iteration. If it does not work, use Newton. PROBLEM 6. (i)...

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