| Week |
Day |
Date |
Notes and readings |
HW |
|
Wed, |
Jan 21 |
Introduction
[Intro][BLAS]
|
|
|
Fri, |
Jan 23 |
Matrix manipulations
[Slides]
|
|
| 2 |
Mon, |
Jan 26 |
Linear algebra review
[NMDS 4.1-4.2][Slides]
|
|
|
Wed, |
Jan 28 |
Linear algebra practice
|
|
|
Fri, |
Jan 30 |
Neumann series, sensitivity, conditioning
|
|
| 3 |
Mon, |
Feb 02 |
Floating point
[Slides (error basics)][Slides (floating point)]
|
|
|
Wed, |
Feb 04 |
Sums, dots, and triangle solves
|
|
|
Fri, |
Feb 06 |
Gaussian elimination
|
|
| 4 |
Mon, |
Feb 09 |
Blocked LU and Cholesky
|
|
|
Wed, |
Feb 11 |
GEPP, backward error analysis, refinement
|
|
|
Fri, |
Feb 13 |
Beyond linear solves + structured solves
|
|
| 5 |
Mon, |
Feb 16 |
February break |
|
|
Wed, |
Feb 18 |
Sparse solves
(Bindel away)
[Slides]
|
|
|
Fri, |
Feb 20 |
Intro to least squares
(Bindel away)
|
|
| 6 |
Mon, |
Feb 23 |
Least squares and QR
|
|
|
Wed, |
Feb 25 |
Ill-posedness and regularization
|
|
|
Fri, |
Feb 27 |
Ill-posedness and regularization
|
|
| 7 |
Mon, |
Mar 02 |
Applications of eigenvalue problems
|
|
|
Wed, |
Mar 04 |
Power iteration
|
|
|
Fri, |
Mar 06 |
From power methods to QR iteration
|
|
| 8 |
Mon, |
Mar 09 |
Hessenberg, tridiagonal, and bidiagonal
|
|
|
Wed, |
Mar 11 |
Stationary iterations
|
|
|
Fri, |
Mar 13 |
Gauss-Seidel convergence, extrapolation
|
|
| 9 |
Mon, |
Mar 16 |
Krylov subspace iterations
(Bindel away)
|
|
|
Wed, |
Mar 18 |
Nonlinear equations in 1D
(Bindel away)
|
|
|
Fri, |
Mar 20 |
Nonlinear equations in 1D
(Bindel away)
|
|
| 10 |
Mon, |
Mar 23 |
Optimization in 1D
|
|
|
Wed, |
Mar 25 |
Nonlinear equations and optimization
(Bindel away)
|
|
|
Fri, |
Mar 27 |
Fixed point iterations and Newton
|
|
| 11 |
Mon, |
Mar 30 |
Spring break |
|
|
Wed, |
Apr 01 |
Spring break |
|
|
Fri, |
Apr 03 |
Spring break |
|
| 12 |
Mon, |
Apr 06 |
Solvers on an autocatalytic example
[Slides]
|
|
|
Wed, |
Apr 08 |
Gradient descent and Newton for optimization
|
|
|
Fri, |
Apr 10 |
Gauss-Newton and nonlinear least squares
|
|
| 13 |
Mon, |
Apr 13 |
Modified Newton iterations
|
|
|
Wed, |
Apr 15 |
Quasi-Newton and other iterations
|
|
|
Fri, |
Apr 17 |
Line search and globalization
|
|
| 14 |
Mon, |
Apr 20 |
Trust regions
|
|
|
Wed, |
Apr 22 |
Homotopy and continuation
|
|
|
Fri, |
Apr 24 |
Constraints and multipliers
|
|
| 15 |
Mon, |
Apr 27 |
Methods for equality constraints
|
|
|
Wed, |
Apr 29 |
Methods for inequality constraints
|
|
|
Fri, |
May 01 |
Derivative free methods
|
|
| 16 |
Mon, |
May 04 |
Review
|
|
|
Sat, |
May 09 |
Final exam at 2 PM
|
|