| LEC # | TOPICS | READINGS |
|---|---|---|
| 1 | Introduction, Basic Linear Algebra | NLA 1 |
| 2 | Orthogonal Vectors and Matrices, Norms | NLA 2 and 3 |
| 3 | The Singular Value Decomposition | NLA 4 and 5 |
| 4 | The QR Factorization | NLA 6 and 7 |
| 5 | Gram-Schmidt Orthogonalization | NLA 8 |
| 6 | Householder Reflectors and Givens Rotations | NLA 10 |
| 7 | Least Squares Problems | NLA 11 |
| 8 | Floating Point Arithmetic, The IEEE Standard | NLA 13, FP |
| 9 | Conditioning and Stability I | NLA 12, 14, and 15 |
| 10 | Conditioning and Stability II | NLA 16 and 17 |
| 11 | Gaussian Elimination, The LU Factorization | NLA 20 and 21 |
| 12 | Stability of LU, Cholesky Factorization | NLA 22 and 23 |
| 13 | Eigenvalue Problems | NLA 24 and 25 |
| 14 | Hessenberg / Tridiagonal Reduction | NLA 26 |
| 15 | The QR Algorithm I | NLA 27 and 28 |
| 16 | The QR Algorithm II | NLA 29 |
| 17 | Other Eigenvalue Algorithms | NLA 30 |
| 18 | The Classical Iterative Methods | It 2.2 |
| 19 | The Conjugate Gradients Algorithm I | NLA 38, CG |
| 20 | The Conjugate Gradients Algorithm II | NLA 38, CG |
| 21 | Sparse Matrix Algorithms | It 4.3, Eig |
| 22 | Preconditioning, Incomplete Factorizations | NLA 40, It 3 |
| 23 | Arnoldi / Lanczos Iterations | NLA 33 and 36 |
| 24 | GMRES, Other Krylov Subspace Methods | NLA 35 and 39, It 2.3 |
| 25 | Linear Algebra Software | Eig |
Table of Contents
Study Materials
Readings
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This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.
The required textbook for this class is:
Trefethen and Bau. Numerical Linear Algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1997, ISBN: 0898713617. (Abbreviated "NLA")
Other readings include:
Bai, et al. Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2000. ISBN: 0898714710. (Abbreviated "Eig")
Barrett, et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1993. ISBN: 0898713285. (Abbreviated "It")
Shewchuk, Jonathan R. "An Introduction to the Conjugate Gradient Method Without the Agonizing Pain." Carnegie Mellon University (August 1994). (Abbreviated "CG") (PDF)#
Goldberg, David. What Every Computer Scientist Should Know About Floating Point Arithmetic. ACM Computing Surveys 23, no. 1 (March 1991): 5-48. (Abbreviated "FP")