## CS 106 Course Diary

 The table below gives a summary of the day-by-day happenings in the lectures for CS 106. The textbook is organized into "lectures", which we can think of as chapters. Textbook sections are shown below as "1", "2", etc. when we refer to an entire chapter and "5.1", "6.2", etc. when we mean a specific section within a chapter.

 Lecture # and Date Topics Covered in This Lecture Corresponding Textbook Sections Homework, etc. 1. Thu Sep 23 Recap of basic linear algebra; linear independence; rank; null spaces 1 HW1 out 2. Fri Sep 24 Further review: inner products; vector norms; induced matrix norms 2, 3 3. Mon Sep 27 A bit about eigenvalues; singular value decomposition 4 4. Wed Sep 29 Relating SVD to rank and eigenvalues; low-rank approximation 5 HW1 in; HW2 out 5. Fri Oct 01 Projectors; Gram-Schmidt; QR factorization 6, 7 6. Mon Oct 04 Modified Gram-Schmidt; more on QR 7, 8 7. Wed Oct 06 Householder triangularization; solving linear systems; least squares 10, 11 HW2 in; HW3 out 8. Thu Oct 07 Flops and operation count; complexity analysis of MGS and Householder (spread out) 9. Fri Oct 08 Condition numbers; definitions and examples 12 10. Mon Oct 11 Floating point arithmetic and roundoff 13 11. Wed Oct 13 Stability; backward stability; analysis of inner product computation 14, 15 HW3 in; HW4 out 12. Fri Oct 15 More on stability; stability of Householder and of back-substitution 16, 17 13. Mon Oct 18 Conditioning of least-squares problems: perturbing b 18 14. Wed Oct 20 Conditioning of least-squares: perturbing A 18 HW4 in; HW5 out 15. Fri Oct 22 (No class; Amit is out of town) 16. Mon Oct 25 (No class; Amit is out of town) 17. Wed Oct 27 Gaussian elimination; LU factorization 20 HW5 in Thu Oct 28 Mid-term exam 18. Fri Oct 29 Partial and full pivoting; stability issues 21, 22 HW6 out 19. Mon Nov 01 Positive definite matrices; Cholesky factorization 23 20. Wed Nov 03 Eigenvalues; non-existence of an exact "algebraic" algorithm 24, 25 21. Fri Nov 05 Hessenberg form; Rayleigh quotients; power iteration 26, 27 HW6 in; HW7 out 22. Mon Nov 08 Converge of Rayleigh quotient iteration; QR algorithm 28 23. Wed Nov 10 QR with shifts 29 24. Thu Nov 11 Analysis of QR with shifts 29 25. Fri Nov 12 Jacobi algorithm; Bisection method; SVD computation 30, 31 HW7 in; HW8 out 26. Mon Nov 15 Arnoldi iteration 33, 34 27. Wed Nov 17 GMRES 35 28. Fri Nov 19 Lanczos and conjugate gradient iterations 36 HW8 in; HW9 out 29. Mon Nov 22 Analysis of CG 38 30. Wed Nov 24 (Thanksgiving break) 31. Fri Nov 26 (Thanksgiving break) 32. Mon Nov 29 More CG analysis; convergence theorems 38 HW9 in 33. Wed Dec 01 Survey of other methods: CGN, BCG, preconditioning 39, 40 Wed Dec 08 Final exam due