Numerical Linear Algebra
- Fall 2017
- Prerequisites: mathematical analysis, advanced linear algebra, matlab
- If any other mathematical topic is as fundamental to the mathematical sciences as calculus and differential equations, it is numerical linear algebra. -- Trefethen & Bau, 1997.
Instructor & Tutor
- Numerical Linear Algebra, Lloyd N. Trefethen and David Bau, III, SIAM, 1997
- (supplement) Applied Numerical Linear Algebra, James Demmel, SIAM, 1997
- (supplement) Numerical Linear Algebra and Applications, Biswa Nath Datta, 2nd Edition, SIAM, 2010
- (supplement) Matrix Computations, Gene H. Golub and Charles F. Van Loan, 4th Edition, Johns Hopkins University Press, 2013
- (supplement) Numerical Linear Algebra with Applications Using MATLAB, William Ford, Academic Press, 2015
- (supplement) MATLAB Primer, Timothy A. Davis, 2011
- Part 1: Inner product, Orthogonality, Vector/Matrix norm, Singular value decomposition (SVD)
- Part 2: QR factorization, Projector, Classical/Modified Gram-Schmidt, Householder reflector, Givens rotation, Least squares
- Part 3: Conditioning, Floating point arithmetic, Stability
- Part 4: LU factorization, Gaussian elimination, Pivoting, Cholesky factorization, Jocabi, Gauss-Seidel and SOR methods
- Part 5: Eigenvalue problem, Power/Inverse iteration, Rayleight quotient iteration, Hessenberg/Tridiagonal reduction, QR algorithm, other algorithms
- Part 6: Other topics depending on time: Krylov subspace methods, Preconditioning, FFT and Structured matrices, Pseudospectra, ...
- Matlab m-files for lectures
Grading policy (tentative)
- Assignment 30% + Programming 30% + Final exam 40%
- Bonus 5% (overall performance: classroom and discussion participation, learning attitude, reading project, ...)
- Assignment + Programming + Bonus <= 60%
- Discussion is permissible. However, transcribed solutions and copied programs are both unacceptable!
- Write solutions of assignments in english and latex are highly encouraged.
- Write programming reports by matlab (you can use matlab's 'publish'). Submit your programming reports to: firstname.lastname@example.org. Only one pdf-file should be submitted with filename studentnumberPx.pdf for Programming x. For example, if your student number is 19020150000000, then your submission for Programming 1 is 19020150000000P1.pdf. Submissions in other file formats are unacceptable!
- Late submissions for assignments and programming reports get only half the score. Unaccepted submissions get 0 score. No exceptions!
- Assignment 1. (latex file) Deadline:
- Assignment 2.
- Assignment 3.
- Assignment 4.
- Assignment 5.
- Programming 1.
- Programming 2.
- Programming 3.
- Programming 4.
- Programming 5.
Reading project (tentative)
- David S. Watkins, The QR algorithm revisited, SIREV, 2008
- Mark Embree, The Arnoldi eigenvalue iteration with exact shifts can fail, SIMAX, 2009
- Jared L. Aurentz and Lloyd N. Trefethen, Block operators and spectral discretizations, SIREV, 2017
- Kui Du, Jurjen Duintjer Tebbens, and Gerard Meurant, Any admissible harmonic Ritz value set is possible for GMRES, ETNA, 2017