Course schedule

LectureDateTopicsHandouts
1Sep 3Introduction
Discretization error
Rounding error
Slides
Condition number notes
2Sep 5The condition number
Floating point arithmetic
Data fitting
Slides
3Sep 10Polynomial interpolation
Chebyshev polynomials
Slides
4Sep 12Lebesgue constant
Splines
Least squares fitting
Slides
Spline notes
Spline fiber ball (MOV)
5Sep 17Underdetermined least squares
Nonlinear least squares
Slides
6Sep 19Numerical linear algebraSlides
Superellipsoids (MOV)
Superellipsoids (MPEG)
7Sep 24LU factorization
Cholesky factorization
Timing algorithms
Slides
8Sep 26QR decomposition
Gram–Schmidt process
Givens rotations
Singular value decomposition
Slides
9Oct 1Low rank approximation
Principal Component Analysis
Numerical calculus
Slides
PCA example
10Oct 3Numerical integration
Gauss quadrature
Slides
Gaussian quadrature notes
11Oct 8Numerical differentiation
ODE Inital Value Problems
Slides
FD stencil notes
12Oct 10ODE convergence
ODE stability
Runge–Kutta methods
Slides
Additional derivations
13Oct 15ODE error estimation
Multi-step methods
Slides
14Oct 17ODE Boundary Value Problems
Hyperbolic PDEs
The CFL condition
Slides
15Oct 22Hyperbolic PDEs
Method of lines
Slides
16Oct 24Parabolic PDEs
Elliptic PDEs
Root finding
Slides
17Oct 29Scalar and vector optimizationSlides
18Oct 31Constrained optimizationSlides
Lagrange multiplier notes
19Nov 5Steepest descent method
Newton method
BFGS optimization
Sequential quadratic programming
Slides
20Nov 7PDE-based optimization
Eigenvalue problems
Slides
21Nov 12Gershgorin theorem
Bauer–Fike theorem
Power iteration
Rayleigh quotient
Slides
22Nov 14QR algorithm
Iterative methods for linear systems
Slides
23Nov 19The multigrid methodNotes
24Nov 21Krylov methodsSlides
Nov 26No lecture
Nov 28Thanksgiving
Dec 3No lecture