Numerical Methods I

Same as COSC3121.03

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. We then turn to the least squares methods for solving overdetermined systems of linear equations. Finally we discuss polynomial interpolations. The emphasis in the course is on the development of numerical algorithms, the use of mathematical software, and the interpretation of the results obtained on some assigned problems.

A possible textbook is Curtis F. Gerald and Patrick O. Wheatley, Applied Numerical Analysis, fifth edition, 1994, Addison Wesley.

The final grade will be based on assignments (including computer assignments), tests and a final examination. Details will be announced. (Same as SC/AS/COSC3121.03.)