Calendar

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

Course Info

Learning Resource Types

assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes