Research Focus Group

Band-Limited Methods and Fast Algorithms

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RFG Info

The general theme of this RFG is to introduce students to recent advances in the field of numerical computation, and the application of numerical techniques to problems in mathematics and engineering. The focus of this RFG will be on band-limited functions and fast algorithms, both of which are closely linked to numerical linear algebra, another active research area pursued at our department. In addition, application of numerical techniques in problems in signal processing, image processing, will be included.

Program Calendar

bulletMAT 290-01/MAT 290-75 Applied Mathematics Seminar (in Conjuction with the Seminar on Band-Limited Methods and Fast Algorithm), Fridays 4:10pm - 5pm, Kerr 693, Fall Quarter. Please visit here for titles and abstracts.
bulletMAT 298-42 Reading Seminar on Scattered Data Analysis, Fall Quarter. Organization Meeting is scheduled on Oct 3rd at 3:10pm in Kerr 693.
bulletReading Seminar on Band-Limited Methods and Fast Algorithms, Winter 2006
bulletReading Seminar on Numerical Methods and Applications, Spring 2006

Organizers

bulletFall Quarter: Professor Naoki Saito , 675 Kerr.
bulletWinter & Spring Quarters: Hong Xiao , 571 Kerr.
bullet Office Hours: by appointment

Reading Seminar on Band-Limited Methods and Fast Algorithms (Organized by Professor Hong Xiao)

In this reading seminar, we will focus on mathematical theory and associated algorithms for approximation, interpolation, integration, and reconstruction of functions with the aid of band-limited functions (that is, functions with compactly supported Fourier transforms). Our motivation comes from the increasing need of accurate and fast numerical algorithms for problems in communication, signal processing, and data analysis.

Topics we wish to cover include:
bullet Fourier Analysis and Sampling Theorem
bulletAlternative Band-Limited Basis, Prolate Spheroidal Wave Functions
bulletInterpolation, Quadratures, Approximation
bulletFast Fourier Transform, Non-equispaced FFT
bulletFast Multipole Methods
bulletRandom Sampling
bulletApplications

Other Information:
bulletCourse Number: MAT 290-64
bulletCRN: 60832 (winter), 80271 (spring)

xiaoh@mathdotucdavis.edu (change "dot" to "." before sending emails) 

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This site was last updated 04/21/06