Readings

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The required textbook for this class is:

Amazon logo Trefethen and Bau. Numerical Linear Algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1997, ISBN: 0898713617. (Abbreviated "NLA")

Other readings include:

Amazon logo 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")

Amazon logo 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")


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