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Unformatted text preview: Numerical Linear Algebra Midterm Exam Take-home Exam Open Notes, Textbook, Homework Solutions Only Calculators Allowed Tuesday 19 October, 2010 Question Points Points Possible Awarded 1. LU 25 2. Structured 30 Factorizations 3. Symmetric Tridiagonal 25 Eigenvalue Problem 4. SVD 30 Total 110 Points Name: Alias: to be used when posting anonymous grade list. 1 Problem 1 (25 points) Let A R n n be a diagonally dominant matrix with A = LU . Suppose you have computed the first i- 1 rows of L and the first i- 1 rows of U by reading and processing the first i- 1 rows of A , i.e., you have not touched rows i to n of A so the algorithm is a delayed update version. 1.a . (15 points) Derive the i-th step of the algorithm where you read row i of A and compute row i of L and row i of U . 1.b . (5 points) Identify the computational primitives used and the level of BLAS in which they appear. 1.c . (5 points) Suppose you want to add pivoting to guarantee stability and existence of the factorization for any nonsingular matrix A . What form of pivoting can be introduced into this algorithm?...
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- Fall '06