Lecture Notes

1 Introduction, Examples, Matrix-Vector and Matrix-Matrix products (PDF)
2 Orthogonal Matrices, Norms of Matrices (PDF)
3 The Singular Value Decomposition (PDF)
4 QR Factorization (PDF)
5 Givens Rotations and Householder Reflections (PDF)
6 Least Squares Problems (PDF)
7 Floating Point Arithmetic (PDF)
8 Conditioning and Stability (PDF)
9 Stability of Givens Rotations and Backward Substitution (PDF)
10 Stability of Least Squares Problems (PDF)
11 Gaussian Elimination (PDF)
12 Cholesky Factorization (PDF)
13 Eigenvalue Problems (PDF)
14 Hessenberg Reduction  
15 QR Algorithm (PDF)
16 Midterm  
17 Stability of the QR Algorithm; Jacobi (PDF)
18 Bisection, Divide and Conquer (PDF)
19 Lanczos, GMRES (PDF)
20 Iterative Algorithms, Arnoldi (PDF)
21 Lanczos Algorithm (PDF)
22 Conjugate Gradients (PDF)
23 Solutions to Ordinary Differential Equations (PDF)
24 Runge Kutta Methods (PDF)
25 Solutions to Stiff ODEs - I (PDF)
26 Solutions to Stiff ODEs - II (PDF)