Quiz! Please write down any material youd like me to cover before - PowerPoint PPT Presentation

Quiz! Please write down any material you’d like me to cover before the midterm on Friday!

Numerical and Scientific Computing with Applications David F . Gleich CS 314, Purdue October 17, 2016 In this class: Eigenvalues and • Review of the eigenvalue the power method problem • Why you should care Next class (a lot!) about eigenvalues. Catchup & Review • How you (probably) G&C – Chapter 12.1.1 learned how to find them • Useful properties of eigenvalues + eigenvectors Next next class Midterm • The power method! G&C – Chapter 6, 7, 12 (sections) • The power method in practice.

An opportunity! I’m giving a lecture tomorrow (10:30-11:30am in LWSN 3102) on how we can use eigenvalues and eigenvectors to find important ecosystems and identify anonomalous groups in Twitter among other things. We will allow up to 15 people (determined by order of emailing the TA with your PUID) to use this lecture to either • Make up a missed class Allow yourself to miss a class during the final week of • mandatory lectures. (But not both). If you interesting, you must receive a slip from us ahead of time (hence the email).

( λ , x ) eigenpair Ax = λ x an important direction det( A − λ I ) = 0 roots of the characteristic polynomial

eigenvalues and eigenvectors show up everywhere

Feedback of speaker & microphone Speaker Microphone Amp d x dt = Ax ( t ) + f ( t )

Gaussian quadrature Z b N X f ( x ) dx ≈ f ( x i ) w i a i =1 x i = nodes w i = weights ( λ 1 , v 1 ), ... , ( λ N , v N ) Eigenvalues, vectors w i = v 2 x i = λ i i ,1

Data analysis

Data analysis

Structural analysis