This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Fall 2009 Name: 3. (10 points) Calculate (by hand) the condition number of the matrix Hint: you may wish to consider the matrix . ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 1 1 1 C . C C T Math 6643 Exam Fall 2009 Name: 4.(10 points) Let A be a symmetric positive definite matrix. Is the Cholesky factorization of A the same as the LU factorization of A? If so, prove it. If not, find a counterexample. Math 6643 Exam Fall 2009 Name: 5. (10 points) Let . ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = 1 1 1 1 1 b D , Find an orthogonal projector onto the Krylov space Db b K , = 2 . Math 6643 Exam Fall 2009 Name: 6. (10 points) Consider the algorithm , where x and c are complex scalars. For which c is the algorithm backward stable? c x fl x f ⊕ = ) ( ) ( ~...
View
Full
Document
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.
 Fall '08
 Staff
 Math, Linear Algebra, Algebra

Click to edit the document details