introductory course in computational linear algebra. Topics include
simple error analysis, linear systems of equations, nonlinear equations,
linear least squares and interpolation. (Same as SC/AS/COSC 3121 3.0.)
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
R.L. Burden and J.D. Faires, Numerical Analysis (6th ed.),
Prerequisite:One of AS/SC/MATH 1010 3.0,
AC/SC/MATH 1014 3.0, AS/SC/AK/MATH 1310 3.0; one
of AS/SC/MATH 1025 3.0, AS/SC/AK/MATH 2221 3.0,
AS/SC/MATH 2021 3.0; one of SC/AS/COSC 1540 3.0,
SC/AS/COSC 2011 3.0 or AS/AK/ITEC 2011 3.0,
SC/AS/COSC 2031 3.0.
Exclusions:SC/AS/COSC 3121 3.0, AK/COSC 3511 3.0.