MATH 3NA3, Winter 2019
NUMERICAL LINEAR ALGEBRA
Why is it good to be well conditioned, but bad to be sensitive? How can you quantify complexity? What do you do when you need to find a solution quickly to a big problem? What is the necessary condition for getting a high paying job? In Math 3NA3 you will learn the answer to these and many more questions. Most problems in physics, engineering and applied mathematics are formulated in terms of equations (e.g. ordinary differential, partial differential, or stochastic) which cannot be solved analytically. However, one can almost always reduce this one difficult problem to many simple problems which can be solved numerically on a computer. More precisely, we reduce the one hard (often impossible) problem to a large system of linear algebraic equations. This course will teach you efficient methods for solving very large systems of linear algebraic equations. With this knowledge as a foundation you will be able to easily tackle any advanced course in scientific computation or numerical analysis. You will also learn the basic mathematical concepts of numerical error analysis (i.e. sensitivity, conditioning and accuracy) and estimation of computational complexity, which are essential for developing a useful and robust numerical algorithm. The course material will be a mix of applied problems, theoretical analysis, algorithm development, and practical programming. Matlab will be the computer language used for all examples and assignments, as it has been developed explicitly for numerical linear algebra. And once you have done this course you will be comfortable in using a computer to solve complex mathematical problems and analyse the results. This is the main skill employers are looking for in a math graduate!
INSTRUCTOR: Chong Wang
Conditioning and numerical stability, rounding and truncation errors, convergence rates, linear and nonlinear systems of equations, eigenvalue problems, least squares, QR and singular-value decomposition, optimization.
Three lectures; one term
Prerequisite(s): MATH 2R03 and one of MATH 1MP3, COMPSCI 1MD3, PHYSICS 2G03
Antirequisite(s): MATH 2T03
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS