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Notes and Resources... are linked from the schedule. Catalog description Gaussian elimination, LUfactorizations and pivoting strategies. Direct and iterative methods for linear systems. Iterative methods for diagonalization and eigensystem computation. Tridiagonal, Hessenberg, and Householder matrices. The QR algorithm. Prerequisites
Computational Resources: You must have access to the current release of Matlab. Class accounts for the labs will be available. You can also use SDSU's Rohan Sun Enterprise system or another capable system. [How to open a ROHAN account]. Students with Disabilities: If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact Student Disability Services at (619)5946473. To avoid any delay, please contact Student Disability Services as soon as possible. Please note that accommodations are not retroactive, and cannot be provided until an accommodation letter from Student Disability Services is received by the Professor. Required Text and Reading Materials: Numerical Linear Algebra, Lloyd N. Trefethen and David Bau, III, Society for Industrial and Applied Mathematics (SIAM), 1997. ISBN 0898713617. Note: SIAM Student Membership is (still, hopefully) FREE, which means you can get the member price! Class web page [http://terminus.sdsu.edu/SDSU/Math543_s2014/], and handouts. Course Outline (as of 1/20/2014): Trefethen/Bau: IFundamentals: MatrixVEctor Multiplication, Orthogonal Vectors and Matrices, Norms, The Singular Value Decomposition, More on the SVD. IIQR Factorization and Least Squares: Projectors, QR Factorization, GramSchmidt Orthogonalization, Householder Triangularization, Least Squares Problems. IIIConditioning and Stability: Conditioning and Condition Numbers, Floating Point Arithmetic, Stability, Stability of Householder Triangularization and Back Substitution, Conditioning of Least Squares Problems, Stability of Least Squares Algorithms. IVSystem of Equations: Gaussian Elimination, Pivoting, Stability of Gaussian Elimination, Cholesky Factorization. VEigenvalues Eigenvalue Problems and Algorithms, Reduction to Hessenberg and Tridiagonal Form, Rayleigh Quotient, Inverse Iteration, QR Algorithm without and with Shifts, Computing the SVD. VIIterative Methods: Overview, Arnoldi Iteration, GMRES, ((Lanczos Iteration)), ((From Lanzcos to Gauss Quadrature)), ((Conjugate Gradients)), ((Biorthogonalization Methods)), ((Preconditioning)). Professor
Peter Blomgren 

Copyright © 2015 Peter Blomgren.
