Course: CAAM 30900=STAT 30900, CMSC 37810
Title: Mathematical Computation 1: Matrix Computation Course
Instructor(s): Lek-Heng Lim
Teaching Assistant(s): Gregory Naisat and Zhisheng Xiao
Class Schedule: Sec 01: MW 3:00 PM–4:20 PM in Rosenwald 015
Textbook(s): Golub, Van Loan, Matrix Computations, 4th edition
Prerequisite(s): Linear algebra (STAT 24300 or equivalent) and some previous experience with statistics
Description: This is an introductory course on numerical linear algebra, which is quite different from linear algebra. We will be much less interested in algebraic results that follow from axiomatic definitions of fields and vector spaces but much more interested in analytic results that hold only over the real and complex fields. The main objects of interest are real- or complex-valued matrices, which may come from differential operators, integral transforms, bilinear and quadratic forms, boundary and coboundary maps, Markov chains, correlations, DNA microarray measurements, movie ratings by viewers, friendship relations in social networks, etc. Numerical linear algebra provides the mathematical and algorithmic tools for analyzing these matrices.
Topics covered: basic matrix decompositions LU, QR, SVD; Gaussian elimination and LU/LDU decompositions; backward error analysis, Gram-Schmidt orthogonalization and QR/complete orthogonal decompositions; solving linear systems, least squares, and total least squares problem; low-rank matrix approximations and matrix completion. We shall also include a brief overview of stationary and Krylov subspace iterative methods; eigenvalue and singular value problems; and sparse linear algebra.