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

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, Runge-Kutta

W

Apr 23

10: Boundary Value Problems for ODEs

F

Apr 25

M

Apr 28

11: Partial Differential Equations

W

Apr 30

F

May 2

M

May 5

Review

W

May 7

12: Fast Fourier Transform

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)

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 2014-04-22 00:57:10 by AndreasKloeckner)