Numerical Methods I


Graduate Division

Computer Science

Cross listed as G63.2010.001, NUMERICAL METHODS I.

Thursday, 5:10-7:00 A. Rangan (fall);
Room 101 Courant.

Prerequisites: a solid knowledge of undergraduate linear algebra, and experience with writing computer programs (in Fortran, C, or other language). Prior knowledge of Matlab is not required, but you will be expected to learn it as the course progresses.

Course Description: Floating point arithmetic; conditioning and stability; numerical linear algebra, including systems of linear equations, least squares, and eigenvalue problems; LU, Cholesky, QR and SVD factorizations; conjugate gradient and Lanczos methods; interpolation by polynomials and cubic splines; Gaussian quadrature. Computer programming assignments form an essential part of the course.

Text:  Numerical Linear Algebra, Trefethen & Bau, SIAM, 1997 (mandatory)

Tentative Syllabus: I will attempt to cover the material in the course description (as well as the textbook). If students are not familar with some fundamental material, I may try and cover/review  those topics as well. Such topics include: Numerical methods for ODEs, Finite difference methods for elliptic PDEs, Fast Fourier Transforms.