Instructor: John Gibson, firstname.lastname@example.org
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 and the eigenvalue problem 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.
|HW4||11/17||conditioning, stability, and accuracy|
|HW5||12/15||Rayleigh quotient iteration and Krylov subspace methods|