574. Numerical Analysis II. This is the second part, independent of the first, of a general survey of the basic topics in numerical analysis. We shall study and analyze a number of numerical algorithms for approximating the solution of a variety of generic problems which occur in applications. The course will begin with the description of the solution methods for the linear system of equations. Starting from the direct methods based on the Gaussian elimination, various classical iterative methods such as Gauss-Seidel, Jacobi and SOR will be discussed. If time permits, we shall also study more advanced iterative methods, multigrid methods in this course, which is known to be most efficient iterative methods until now. Large portion of the course will be devoted to numerical techniques for optimization, matrix eigenvalues and eigenvectors and numerical solutions to nonlinear equations. As a separate but important technique, finite difference and finite element discretization methods for simple partial differential equations such as Poisson's equations and Heat equations will be studied at the end of the course. Particular emphasis in this course is to interconnect the theorectical results and computer implementation. Students will study not only the solid theoretical backgrounds in developing and understanding the algorithms but also a hands-on experience to implement the methods.

(1) A. Quarteroni, R. Sacco, and F. Saleri Numerical Mathematics, 2nd Ed., Springer, 2004
(2) K. Atkinson An Introduction to Numerical Analysis, 2nd Ed., Wiley, 1989


Note* : Most of lectures will be based on hand outs prepared by the instructor. Students are suggested to have one of the aforementioned textbooks depending on their preference.

Homework assignments in the course consist of both theoretical and computational work. For the computational component, the students should use a language/environment that possesses high level data types so that the students spend more time working with algorithms and not worrying about the details of writing computer code. Matlab is a good choice. Fortran 77/90/95 and C++ with appropriate class libraries can also be used.

Advanced Calculus, Linear Algebra, and familiarity with differential equations. Numerical Analysis 01:642:573 is desirable but not required.

Topics listed above is temporary and may be modified.