York Calendar Description An introductory course in computational
linear algebra. Topics include simple error analysis, linear systems of
equations, nonlinear equations, linear least squares and interpolation. (Same
Prerequisites: One of MATH1010.03, MATH1014.03, MATH1310.03; one ofMATH1025.03,MATH2021.03, MATH2221.03; one of COSC1540.03, COSC2011.03, COSC2031.03.
Expanded description The course begins with a general discussion of computer arithmetic and computational errors. Examples of ill-conditioned problems and unstable algorithms will be given. The first class of numerical methods we introduce are those for nonlinear equations, i.e., the solution of a single equation in one variable. We then turn to a discussion of the most basic problem of numerical linear algebra: the solution of a linear system of n equations in n unknowns. The Gaussian elimination algorithm will be discussed as well as the concepts of error analysis, condition number and iterative refinement. Then we discuss polynomial and spline interpolation. We then turn to the least squares methods for solving over determined systems of linear equations, with a brief introduction to approximation theory. The emphasis in the course will be on the how, why and when of numerical approximation techniques. We will also discuss the development of numerical algorithms, and the use of mathematical software.
The textbook is Numerical Analysis by Richard L. Burden and J. Douglas Faires, 7th ed, Brooks/Cole Publishing Company, 2001 [Parts ofChapters1,2,6,3,7,8]
Webresources related to the course(some links may be out of date)
Revised September 9, 2002