FSF3580 Numerical Linear Algebra
KTH Royal Institute of Technology
This course is designed for PhD students in applied and computational mathematics, but it is suitable also for other PhD students with a background in computation with mathematical interests. The students are expected to have taken basic and a continuation course in numerical analysis or acquired equivalent knowledge in a different way.
In this course the students will learn a selection of the most important numerical methods and techniques from numerical linear algebra. This includes detailed understanding of state-of-the-art iterative algorithms as well as improvements and variants. Convergence theory and practical implementation issues for specific problems are addressed. The course consists of a number of blocks:
- Numerical methods for large-scale eigenvalue problems
- Numerical methods for large-scale linear systems of equations
- Numerical methods for functions of matrices
- Numerical methods for matrix equations
- Individual project related to numerical linear algebra
After completion of the course, the students are expected to be able to:
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apply, extend and generalize the main numerical methods: Arnoldi's method, Rayleigh quotient iteration, GMRES, CG, BiCG, CGN, QR-method, scaling-and-squaring, Denman-Beavers algorithm and Parlett-Schur
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interpret, apply and generalize convergence theory for the iterative algorithms:
- Characterization of convergence order and convergence factors of all covered methods
- Explicit min-max-bounds and condition number bounds for Arnoldi, GMRES, CG, CGN and QR-method
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relate and motivate how (or why not) the methods in this course can be used in their PhD topic
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