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 * [[attachment:project.pdf|Project for 4 credit hours]] (Grad students only · Due: May 14, 2014 · Progress report due: April --(16)-- '''21''', 2014 · Out: March 18, 2014) [[attachment:project-starter.zip|Project starter kit]]  * [[attachment:project.pdf|Project for 4 credit hours]] (Grad students only · Due: May --(14)-- '''16''', 2014 · Progress report due: April --(16)-- '''21''', 2014 · Out: March 18, 2014) [[attachment:project-starter.zip|Project starter kit]]

Textbook cover

Numerical Analysis (CS 450)

Class Time/Location

MWF 9:00am-9:50am / 1310 DCL

Class Webpage

http://bit.ly/cs450-s14

Web forum

Piazza

Homework submission/grades

UIUC Moodle

Team

Andreas Kloeckner

Instructor

Andreas Kloeckner

Email

andreask@illinois.edu

Office

4318 Siebel

Office Hours

Mondays and Wednesdays 10:00 am to 11:00 am (after class)

Kaushik Kalyanaraman

TA

Kaushik Kalyanaraman

Email

kalyana1@illinois.edu

Office

0207 Siebel

Office Hours

Mondays 12:45 pm to 1:45 pm; Wednesdays 3:00 pm to 4:00 pm

Sweta Seethamraju

TA

Sweta Seethamraju

Email

seetham2@illinois.edu

Office

0207 Siebel

Office Hours

Mondays and Tuesdays 2:00 pm to 3:00 pm

Textbook/Material

Updates/Calendar

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

Class Material

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

Grading

Homework/Quizzes

30%

Exam #1

20 %

Exam #2

20 %

Final Exam

30 %

Probable grading scale:

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.

    [End addition]

  • 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.

Previous editions of this class

Python Help

Numpy Help

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