# Numerical Analysis (CS 450)

 Class Time/Location MWF 9:00am-9:50am / 1310 DCL Class Webpage Web forum Homework submission/grades

## Team

 Instructor Email Office 4318 Siebel Office Hours Mondays and Wednesdays 10:00 am to 11:00 am (after class) TA Kaushik Kalyanaraman Email Office 0207 Siebel Office Hours Mondays 12:45 pm to 1:45 pm; Wednesdays 3:00 pm to 4:00 pm TA Sweta Seethamraju Email Office 0207 Siebel Office Hours Mondays and Tuesdays 2:00 pm to 3:00 pm

## Textbook/Material

January 22, 2014 (Wedensday)
Class starts at 9am. See you then, bright and early!

## Homework

Homework solutions (private, same password as slides)

## Schedule

 Date Chapter Topic W Jan 22 1: Intro Introduction, fw/bw error F Jan 24 Fw/bw error, conditioning, intro floating point M Jan 27 Floating point W Jan 29 2: System of Linear Equations Cancellation, Intro LA F Jan 31 LA conditioning, Intro Gaussian el. M Feb 3 Gaussian el, preconditioning, pivoting W Feb 5 LA cost, Sherman-Morrison F Feb 7 3: Linear least squares BLAS, Intro least squares M Feb 10 Normal equations W Feb 12 QR, QR via Gram-Schmidt F Feb 14 Householder, Givens, Rank-deficiency M Feb 17 4: Eigenvalues and singular values SVD, Intro eigenvalues, Sensitivity W Feb 19 Transforms, Schur form, Power iteration F Feb 21 Rayleigh quotient it, Intro QR it. M Feb 24 QR iteration W Feb 26 5: Nonlinear equations Krylov space methods, Intro root finding F Feb 28 Contractive mappings, convergence rates, sensitivity of root finding M Mar 3 Stopping criteria, Bisection, Fixed point iteration, Newton W Mar 5 Exam 1 Chapters 1-4, in-class. F Mar 7 6: Optimization Secant method, Newton and Secant-updating methods in nD, Intro Optimization M Mar 10 Existence/uniqueness of minimizers, sensitivity of opt. W Mar 12 Discussion of exam 1, Golden Section Search, Newton for Optimization F Mar 14 No class Engineering Open House M Mar 17 6: Optimiziation Steepest descent, Newton, Nelder-Mead W Mar 19 Gauss-Newton, Levenberg-Marquardt, Constrained opt F Mar 21 7: Interpolation Constrained opt, Intro Interpolation M Mar 24 No class Spring Break W Mar 26 F Mar 28 M Mar 31 7: Interpolation Lagrange basis, Orthogonal polynomials W Apr 2 8: Numerical Integration and Differentiation Interp. error, Piecewise interp., Intro Quadrature F Apr 4 Newton-Cotes, accuracy and stability of quadrature M Apr 7 Composite and Gaussian quadrature W Apr 9 9: Initial Value Problems for ODEs Numerical differentiation, Richardson extrapolation, Intro IVPs F Apr 11 IVP terminology, stability, examples M Apr 14 Euler's method, accuracy, stability W Apr 16 Exam 2 Chapters 5-8, in-class. F Apr 18 9: Initial Value Problems for ODEs Exam 2 discussion, implicit methods, backward Euler M Apr 21 Stiff problems, Predictor-Corrector W Apr 23 10: Boundary Value Problems for ODEs Runge-Kutta, Stability regions F Apr 25 Intro BVPs, Existence, Uniqueness, Conditioning, Shooting Method M Apr 28 11: Partial Differential Equations Shooting, Sparse Matrices, Finite Difference Method, Intro FEM W Apr 30 FEM/Galerkin, sparse linear algebra F May 2 Stationary methods, Jacobi, Gauss-Seidel, SOR, Conjugate Gradients M May 5 PDEs: consistency, stability, time integration W May 7 Review (see study guide posted above) W May 14 Final exam at 1:30-4:30 PM

 Homework/Quizzes 30% Exam #1 20 % Exam #2 20 % Final Exam 30 %

 graduate undergraduate A [90, 100) [85, 100) B [80, 90) [72, 85) C [70, 80) [60, 72) D [60, 70) [50, 60)
• Late Work policy: Work submitted after the deadline will count for half of its original worth. This offer is good for up to one week after the original deadline. After that, no late work will be accepted.

[Added to clarify on 2/13] You get exactly one submission per homework set. In particular, this means that:

• No regrading of work already graded. If, between the posted solution and your graded work, you still have questions, feel free to raise those on Piazza or during the TA's office hours.
• We do not accept partial submissions unless you have a very good reason. (e.g. we won't let you submit problem 1 and 2 before and 3,4,5 after the deadline.) If you modify your submission after the deadline but before it's graded, your entire submission will be counted as late.
In addition, the grading policy is set up so that you can mess up on the homework quite badly without a drastic impact on your grade. The homework is *intended* as a learning experience, so making mistakes is OK.

• Make-up exam policy: Make-up exams must be requested at least one week before the original or make-up date, whichever is sooner.

• Taking the class for 4 credits: Grad students may take CS450 for four credit hours. To this end, an individual project will be assigned around the beginning of March. An initial draft of the report on the project will be due on April 16. The final version of the report (along with all further deliverables, such as code) is due on the day of the final, May 14. The project will count as an extra homework set with double weight.

• Please let me (Andreas) know as soon as you can if you need special accommodations (extra time etc.) on exams. Thanks!

## Computing

We will be using Python with the libraries numpy, scipy and matplotlib for in-class work and assignments. No other languages are permitted. Python has a very gentle learning curve, so you should feel at home even if you've never done any work in Python.

### Virtual Machine Image

See ComputeVirtualMachineImages to obtain a virtual machine image that you can use to follow the computational exercises in the class and do your homework.

## Python Help

### Numpy Help

Teaching/NumericalAnalysisSpring2014 (last edited 2014-05-13 23:07:29 by AndreasKloeckner)