This course is concerned with the understanding and application of algorithms for scientific computing. Among the topics that will be discussed in the course are computer arithmetic, the solution of linear systems of equations, the solution of overdetermined systems by the least-squares method, the singular value decomposition, approximation and interpolation, curve fitting, numerical integration, eigenvalue problems, as well as the solution of nonlinear systems of equation. Numerous illustrations of how the numerical methods discussed work in practice will be provided. Several projects that require the development of software for scientific computing will be assigned. The programming langauge MATLAB will be taught and most of the computations will be carried out in Matlab or GNU Octave.

MATH/CS 62251/72251: Numerical Analysis I

The material covered in this course is essential for the understanding and proper use of most state-of-the-art numerical methods and software for scientific computing. The course emphasizes fundamental algorithms of linear algebra and their many applications. A geometric approach helps to provide a thorough understanding of the underlying concepts. Matrix factorization methods will be emphasized. Methods for least squares problems, eigenvalue and singular value computation, and the solution of so-called inverse problems, with application to image restoration, will be discussed. MATLAB or GNU Octave implementation of algorithms will provide valuable hands-on experience.