CSC 80040: Topics in Algorithm Design - Algebraic and Numerical Computation

Prof. V. Pan
Tues., 6:30 - 8:30PM
3 cr., Rm. TBA

The fields of algebraic and numerical computing are the cornerstone of modern computations in sciences, engineering, and signal processing.  The seminar enables rapid advance in both study and research by merging the most effective methods in both fields. This relatively recent direction has been well recognized by now, but fresh research topics are still abundant. Both Computer Science and Mathematics students can join the seminar for learning and/or research, le! ading to dissertations (17 PhD defenses in the last 9 years in both programs). The subjects in the seminar can be partly adjusted to the students' interests and background.

 
Recently covered topics include:

a) Structured (e.g., Toeplitz, Hankel, Cauchy,  Pick, and semiseparable) matrices. They are omnipresent in modern computations as well as in many areas of math, and they are closely related to fundamental algebraic computations with polynomials and rational functions.

b) Recent novel methods for the algebraic eigenproblem, which is one of the two most fundamental computations in linear algebra. 

c) Solving a polynomial equation, which was the central and most influential problem in math for 4 millennia and is still highly important in computer algebra. Some extensions to the fundamentals of the solution of systems of multivariate polynomial equations have been studied! .

d) Polynomial and rational interpolation.
e) Algebraic techniques for coding and cryptography.
f) Fast and certified computation of the sign of the determinant, with applications to some fundamental geometric computations.

 
The seminar resumes with new topics every semester. Some students continue to attend  and get 3 credits every semester.

The students are divided into the entry level group and the advanced group.  The instructor usually meets separately for two hours per week with each group. The the entry level students eventually join the group of advanced students.

 
Survey and research papers are supplied as handouts. Some relevant papers are available at the instructor's homepage at http://comet.lehman.cuny.edu/vpan/ and some as his Tech Reports at the CS De! pt. in the Graduate Center. The students can also use the texts published by the instructor and available in the GC library.

 
The Computer Science students are encouraged to implement new algorithms devised in the seminar, and the Math students to solve the relevant open problems in math. The successful results become parts of the theses and research articles.

Last Modified on: 09/09/2006

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