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Unformatted text preview: Numerical Linear Algebra Midterm Exam Takehome Exam Open Notes, Textbook, Homework Solutions Only Calculators Allowed No collaboration with anyone Due beginning of Class Wednesday, October 26, 2011 Question Points Points Possible Awarded 1. Structured Schur 25 complements 2. LU 30 Factorizations 3. Kronecker Product 25 Factorizations 4. Lowrank 25 Displacement 5. Sparse Primitives 25 Total 130 Points Name: Alias: to be used when posting anonymous grade list. 1 Problem 1 1.a (10 points) Suppose A R n n . Define A (0) = A and denote by A ( k ) the Schur complement of A ( k 1) with respect to e T 1 A ( k 1) e 1 for k = 1 ,...,n 1. For each 0 k n 1, let k be the maximum magnitude of all the elements in A ( k ) . Define a growth factor for the series of Schur complements as = max k n 1 k . Determine for the symmetric matrix A = 1 1 1 1 1 2 2 2 1 2 3 3 1 2 3 4 ....
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This note was uploaded on 11/10/2011 for the course MAD 5932 taught by Professor Gallivan during the Fall '06 term at FSU.
 Fall '06
 gallivan

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