This graduate level course provides an introduction to numerical linear algebra. The course focuses on numerical solutions to classic problems of linear algebra. Topics include LU, Cholesky and QR factorizations, iterative methods for linear equations, least square, power methods and QR algorithm for eigenvalue problems, conditioning and stability of numerical algorithms. 

Instructor: Qi Gong (qigong@soe.ucsc.edu) Office: Baskin Engineering 361A

Textbook: Numerical Linear Algebra, Lloyd Trefethen and David Bau. SIAM, ISBN-13: 978-0898713619, ISBN-10: 0898713617

Supplementary Reading Material

• Applied Numerical Linear Algebra, James W. Demmel, SIAM, ISBN-13: 978-0898713893, ISBN-10: 0898713897

• Matrix Computations, Gene H. Golub and Charles F. Van Loan, Johns Hopkins University Press, ISBN-10: 1421407949, ISBN-13: 978-1421407944

Lectures: Monday, Wednesday, Friday, 11:00AM - 12:10PM, BE 169

Office Hours: Monday 2:00PM - 3:30PM, BE 361A

Grading: Homework 60%, Final exam 40%.

Academic Honesty: see explanation at http://www.ucsc.edu/academics/academic_integrity/index.html 

Tentative Schedule

• Week 1: Introduction to numerical linear algebra and review of linear algebra. Read Lecture 1 - 3 and Lecture 13 of the textbook. 
• Week 2: Matrix norm, Singular Value Decomposition, and QR factorization. Read Lecture 4 - 5 and Lecture 7 of the textbook.
• Week 3: QR factorization by Gram-Schmidt orthogonalization and Householder transformation. Read Lecture 6, 8 - 10 of the textbook.
• Week 4: Least squares problems, conditioning and condition number. Read Lecture 11 - 12 of the textbook.
• Week 5: Conditioning of least squares problems, stability and backward stability. Read Lecture 14-19 of the textbook.
• Week 6: Gaussian elimination, LU factorization, and Cholesky factorization. Read Lecture 20 - 23 of the textbook.
• Week 7: Eigenvalue/eigenvector problems: power iteration, inverse iteration, reduction to Hessenberg form. Read Lecture 24 - 27 of the textbook.
• Week 8: QR algorithm for eigenvalue problems, Singular Value Decomposition. Read Lecture 28 - 31 of the textbook.
• Week 9: Iterative methods for linear systems: Jacobi, Gauss-Seidal, SOR iterations, steepest descent and conjugate gradient methods. Read Lecture 32 and 38 of the textbook.
• Week 10: Convergence analysis of conjugate gradient method, Arnoldi iteration, GMRES, and iterative methods for eigenvalue problems. Read Lecture 33, 34, and 35 of the textbook.

Students with disabilities: If you qualify for classroom accommodations because of a disability, please get an Accommodation Authorization from the Disability Resource Center (DRC) and submit it to me in person outside of class (e.g., office hours) within the first two weeks of the quarter. Contact DRC at 459-2089 (voice), 459-4806 (TTY), or http://drc.ucsc.edu for more information on the requirements and/or process.