Required Textbook: Numerical Linear Algebra, by L.N. Trefethen and D. Bau III, SIAM 1997.
Course Objectives: To provide an introduction to numerical methods for solving linear equations and the eigenvalue problem. In addition, it provides necessary background for graduate students interested in numerical analysis research.
Synopsys: Common problems in linear algebra. Matrix structure, singular value decomposition. QR factorization, the QR algorithm for eigenvalues. Direct solution methods for linear systems, Gaussian elimination and its variants. Iterative solution methods for linear systems.
Files for the experiments in Lecture 9 :
Matrices for Gram-Schmidt algorithms: GS
Data for Lab #4
Routines rounding errors, chop, sum order and unit round for Lab #5.
Papers and resources:
A MATLAB primer:
Other MATLAB tutorials :
Applied Numerical Linear Algebra, by J. W. Demmel, SIAM 1997
Matrix Computation, by G. H. Golub and F. Van Loan, 1996
Fundamentals of Matrix computation, D. Watkins, SIAM 1997