LEC # | TOPICS | KEY DATES |
---|---|---|
Week 1 covers Lectures 1 and 2. | ||
1 | Course overview, Newton’s method for root-finding | |
2 | Floating-point arithmetic | |
Week 2 covers Lectures 3–5. | ||
3 | Floating-point summation and backwards stability | |
4 | Norms on vector spaces | |
5 | Condition numbers | Problem set 1 due |
Week 3 covers Lectures 6–8. | ||
6 | Numerical methods for ordinary differential equations | |
7 | The SVD, its applications, and condition numbers | |
8 | Linear regression and the generalized SVD | |
Week 4 covers Lectures 9–11. | ||
9 | Solving the normal equations by QR and Gram-Schmidt | |
10 | Modified Gram-Schmidt and Householder QR | |
11 | Matrix operations, caches, and blocking | Problem set 2 due |
Week 5 covers Lectures 12–14. | ||
12 | Cache-oblivious algorithms and spatial locality | |
13 | LU factorization and partial pivoting | |
14 | Cholesky factorization and other specialized solvers. Eigenproblems and Schur factorizations | |
Week 6 covers Lectures 15–17. | ||
15 | Eigensolver algorithms: Companion matrices, ill-conditioning, and Hessenberg factorization | |
16 | The power method and the QR algorithm | |
17 | Shifted QR and Rayleigh quotients | Problem set 3 due |
Week 7 covers Lectures 18–20. | ||
18 | Krylov methods and the Arnoldi algorithm | |
19 | Arnoldi and Lanczos with restarting | |
20 | The GMRES algorithm and convergence of GMRES and Arnoldi | Final project proposal due |
Week 8 covers Lectures 21–23. | ||
21 | Preconditioning techniques. The conjugate-gradient method | |
22 | Convergence of conjugate gradient | |
23 | Biconjugate gradient algorithms | Problem set 4 due |
Week 9 covers Lectures 24–26. | ||
24 | Sparse-direct solvers | |
25 | Overview of optimization algorithms | Take-home midterm exam due before Lec #25 |
26 | Adjoint methods | |
Week 10 covers Lectures 27 and 28. | ||
27 | Adjoint methods for eigenproblems and recurrence relations | |
28 | Trust-regions methods and the CCSA algorithm | |
Week 11 covers Lectures 29–31. | ||
29 | Lagrange dual problems | |
30 | Quasi-Newton methods and the BFGS algorithm | |
31 | Derivation of the BFGS update | |
Week 12 covers Lectures 32–34. | ||
32 | Derivative-free optimization by linear and quadratic approximations | |
33 | Numerical integration and the convergence of the trapezoidal rule | |
34 | Clenshaw-Curtis quadrature | |
Week 13 covers Lectures 35–37. | ||
35 | Chebyshev approximation | |
36 | Integration with weight functions, and Gaussian quadrature | |
37 | Adaptive and multidimensional quadrature | |
Week 14 covers Lectures 38 and 39. | ||
38 | The discrete Fourier transform (DFT) and FFT algorithms | |
39 | FFT algorithms and FFTW | Final project due at the end of term |
Calendar
Course Info
Instructor
As Taught In
Spring
2019
Level
Topics
Learning Resource Types
assignment_turned_in
Problem Sets with Solutions
grading
Exams with Solutions
notes
Lecture Notes