General description
The course will go through numerical algorithms for solving problems in linear algebra, including linear systems of equations, eigenvalue problems, singular value decomposition, and least squares problems. Beside classical topics (e.g. GE, LU, Cholesky, Jacobi, Gauss-Seidel, CG, GMRES, domain decomposition, multigrid, preconditioning, power method, QR, Arnoldi, Lanczos, FFT, etc...), we will also discuss more recent techniques (such as Hierarchical matrices and randomized low rank approximations). The focus will be on understanding stability, errors, complexity, and implementation issues for the algorithms. We will be using Matlab throughout the course.Syllabus (updated in April)
Instructor
Mohammad Motamed
Instructor's office hours
1) Tu 14.00-15.30 2) Th 14.00-15.30 3) by appointment
Required literature
1) D: James Demmel. Applied Numerical Linear Algebra. SIAM. 1997. (Also note errata page.) 2) NMT: N. Halko, P.-G. Martinsson and J. A. Tropp. Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions, SIAM Review, 57(2):217-288, 2011. 3) BGH: S. Borm, L. Grasedyck and W. Hackbusch. Hierarchical Matrices, Lecture Notes 21, MPI Leipzig, 2003.
Lecture notes
Introduction: notesLinear Systems (direct methods): notes
Linear Systems (iterative methods): notes on classical methods, notes on Krylov methods and multigrid
Eigenproblems: notes 1 notes 2
Singular Value Decomposition: notes
Least Squares Problems: notes
Low-rank approximation by Hierarchical Metrices: notes
Homework
Homework Report Format HW1 (due extended to Feb. 19th) Files: eiffel1.mat eiffel2.mat eiffel3.mat eiffel4.mat trussplot.m HW2 (due extended to April 18th) Files: cooling_flange.mat convdiff.mat lap.m HW3 (Email your report on May 9th before 23:59) Files: illposed.mat hmatrix.mat
NEWS
motamed@math.unm.edu
Last updated: Spring 2019