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AMCS 251

AMCS 251 -  Numerical Linear Algebra By Prof. David Isaac Ketcheson

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Most mathematical models cannot be solved exactly; their solution must be approximated. Nearly all methods of approximation consist of transforming the problem to a system of linear algebraic equations. These systems are usually large and they also cannot be solved exactly, but must be approximated. The study of their solution is known as linear algebra, and it forms the backbone of nearly all computational mathematics, from optimization, to PDEs, to statistics, and beyond.
This course will introduce you to the essential problems and solution techniques of numerical linear algebra, including square linear systems, eigenvalue problems, and least squares. When the first computers became available for solving linear algebraic systems, the experts predicted that computed solutions of large systems would be useless due to the amplification of errors. Nevertheless, numerical solution of very large linear systems has become an essential tool underlying things that we all use every day. In this course, you will learn how those solutions are computed. The material is based closely on the text of Trefethen and Bau.

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