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**Gilbert Strang**

**Wavelets and Mesh Generation**

**Wednesday, January 12,** **2005**

**Building 3 Auditorium - 3:30 PM**

(Refreshments at 3:00 PM)

Dr. Gilbert Strang, will talk about Wavelets and Mesh Generation. Professor Strang will describe the construction of wavelets (including lifting schemes) and he will discuss their applications in data compression and scientific computing. It is natural to compare their properties with the Fourier basis -- especially with the Discrete Cosine Transform. The Discrete Wavelet Transform is a "short-time" alternative to the DFT/DCT, giving more information about time and scale (and chosen for JPEG2000). The choice of a basis, in other words the decision on how to represent the signal, the image, or the solution, is fundamental.

An essential first step in many problems of numerical analysis and computer graphics is to cover a region with a reasonably regular mesh. Professor Strang will describe a short MATLAB code that begins with a "distance function" to describe the region: d(x) is the distance to the boundary (with d < 0 inside the region). The algorithm decides the location of nodes and the choice of edges. At each iteration the mesh becomes a truss (with forces in the edges that move the nodes). Then the Delaunay algorithm resets the topology (the choice of edges). The input includes a size function h(x) to vary the desired meshlengths over the region.

The code is adaptable and public (math.mit.edu/~persson/mesh). It extends directly to n dimensions. The 2D meshes are remarkably regular. In higher dimensions, it is difficult to avoid "slivers".

References:

Wavelets and Filter Banks, Gilbert Strang and Truong Nguyen, Wellesley-Cambridge Press.

A simple mesh generator in MATLAB, Per-Olof Persson and Gilbert Strang, SIAM REVIEW 46 (2004) 329-345.

Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT and an Honorary Fellow of Balliol College.

Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and six textbooks:

Introduction to Linear Algebra (1993, 1998, 2003), Linear Algebra and Its Applications (1976, 1980, 1988), Introduction to Applied Mathematics (1986), Calculus (1991), Wavelets and Filter Banks, with Truong Nguyen (1996), Linear Algebra, Geodesy, and GPS, with Kai Borre (1997)

Gilbert Strang served as President of SIAM during 1999 and 2000. He is Chair of the US National Committee on Mathematics for 2003-2004. His home page is http://math.mit.edu/~gs and his courses are on http://ocw.mit.edu

IS&T Colloquium Committee Host: Jacqueline Le Moigne