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Comments and Announcements about course on Spectral Methods - Fall 2010, Technion

The course is taught by Prof Eli Ben Sasson and Dr. Ariel Gabizon at Taub 8 , Tuesdays 10:30-12:30.
The course mostly follows the notes of Dan Spielman:

Links relating to lectures

posted Jan 11, 2011, 4:47 AM by Ariel Gabizon

Last week David talked about this paper

Today I talked about the following graph isomorphism paper:

Last HW assignment

posted Jan 11, 2011, 4:46 AM by Ariel Gabizon

For the third and last HW assignment in this course please submit by the end of the semester problem 1 in problem set 3 and problems 1-3 in problem set 4 on Dan's course website:

Lectures in December

posted Dec 22, 2010, 9:40 AM by Ariel Gabizon   [ updated Dec 22, 2010, 10:03 AM ]

In previous recent meetings Eli Discussed efficient approximation for linear equations, following
lectures 15-16 of Spielman.

The lecture this Tuesday Dec 21st was based on the following paper
We continue reviewing this paper next Tuesday.

p.s.- will probably return ex. 1 next Tuesday

5th lecture - Novemeber 16th

posted Nov 16, 2010, 10:07 AM by Ariel Gabizon   [ updated Nov 16, 2010, 10:09 AM ]

Eli covered Lecture 5 in the notes.

Here is the link to the talk of Dan Spielman Eli mentioned

Third Lecture - November 2nd

posted Nov 2, 2010, 8:47 AM by Ariel Gabizon

I discussed the Perron-Frobenius Theorem. A simpler proof  in my opinion for positive matrices, without subtle analysis points, can be
found here starting from slide 19.
Eli followed Lectures 12-13 from a different course by Spielman, this one:

The first homework set, due in two weeks (Nov 16) is Problem set 1 from Dan's course, here's a link:

Comments about second lecture, Tuesday Oct 28th

posted Nov 1, 2010, 12:54 AM by Ariel Gabizon   [ updated Dec 22, 2010, 10:03 AM ]

The material we covered is the second half of Lecture 2 and first half of Lecture 3 in Spielman's notes.

-(note that below I use C(i,j) for the (i,j)'th entry in the matrix C, as opposed to class where I used subscripts)

1. We proved Feidler's Theorem that for a Laplacian of a weighted path, an eigenvector of the k'th smallest eigenvalue changes sign *at most* times.
I stated this as *exactly* k times, but as was noted in class this does not make sense when the eigenvalue has multiplicity>1. So what is correct is the `at most' statement,
and the `exactly' statement is true only when the k'th smallest eigenvalue has multiplicity one.

2. I had a problem with the proof of the above theorem at the following point: We had a symmetric matrix C such that for any vector x  x^T*C*x = \sum_i lambda_i *(x_i)^2.
I  wanted to say that this implies the lambda_i's are eigenvalues of C. This is true since in the bilinear form x^T*C*x, for a symmetric C, the coefficient of x_i*x_j is 2*C(i,j) , so the equality above implies C is a diagonal matrix with C(i,i) =lambda_i in the diagonal. What I claimed about certain unit vectors being eigenvectors was not true.

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