Content
Course Description:
This course is a fundamental course in numerical analysis focusing on numerical linear algebra, which is the building block for a variety of algorithms used in engineering and computational science problems. The goal is to help students to gain a through understanding of useful tools from numerical point of view, and provide students the essential ideas to work effectively with vectors and matrices through focus on practical algorithmic ideas.
Topics include introduction on numerical analysis and numerical linear algebra, review on fundamental linear algebra such as singular value decomposition, direct solvers such as Gaussian elimination, various iterative methods such as conjugate gradient methods, and possibly least squares problems and eigenvalue methods.
Please note that the above syllabus is tentative and might change during the term.
Textbook:
The course will not follow closely a specific textbook. Here are some recommended references.
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Numerical Linear Algebra. Lloyd N. Trefethen and David Bau, III, SIAM.
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A First Course in Numerical Methods. Uri M. Ascher and Chen Greif, SIAM 2006.
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Numerical Mathematics. Alfio Quarteroni, Riccardo Sacco and Fausto Saleri, Springer.
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An Introduction to Numerical Analysis. Kendall E. Atkinson, Wiley.
MATLAB resources:
Matlab will be used for the computer assignments. Some good MATLAB references could be found here and here.