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IAM 961: Numerical Linear Algebra

Instructor: John Gibson,
Office hours: Tue 2-3pm, Thu 12-1pm, Kingsbury N309E, or after class

Numerical linear algebra is the science of solving systems of linear equations $Ax=b$ and the eigenvalue problem $A v = \lambda v$ on a digital computer –problems are at the root of the vast bulk of scientific computation. Compared to classical linear algebra, the finite precision and computational cost of numerical mathematics brings in a number of important new concepts, including conditioning, stability, and accuracy, and efficiency. We will develop these ideas and learn the most important numerical linear algebra algorithms: QR, LU, SVD decompositions, Gramm-Schmidt orthogonalization, the QR eigenvalue algorithm, and Krylov subspace methods. Time permitting, we will also study key algorithms for function optimization and the solution of systems of nonlinear equations.

Text: Numerical Linear Algebra, by Trefethen and Bau, SIAM Press.

Course outline


lecture notes date
SVD demo 09/24
HW due topic comments
HW1 9/22 norms
HW2 10/06 SVD
HW3 10/20 QR algorithms
HW4 11/17 conditioning, stability, and accuracy
HW5 12/15 Rayleigh quotient iteration and Krylov subspace methods
exam date comments
final t.b.d.
gibson/teaching/fall-2014/iam961.txt · Last modified: 2014/12/05 13:47 by gibson