Instructor: John Gibson, Kingsbury N309E, john.gibson@unh.edu

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 speed 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.