Week of February 9 - 13, 1998

Monday, February 9

11:30 MATHEMATICS EDUCATION SEMINAR  - Room 447 MSC
      Barbara Moses, Dept. of Mathematics and Statistics, BGSU. 
      "Practical applications of constructivism in the mathematics 
       classroom"

 2:30 ALGEBRA SEMINAR  - Room 447 MSC
      Curt Bennett, Dept. of Mathematics and Statistics, BGSU. 
      "Buildings: an introduction"

 2:30 ANALYSIS SEMINAR  - Room 459 MSC
      Alex Izzo, Dept. of Mathematics and Statistics, BGSU. 
      "More on the d-bar equation"

 3:30 STATISTICS SEMINAR SERIES  - Room 459 MSC
      Jiahua Chen, University of Waterloo, visiting BGSU this semester
      "Empirical Likelihood Methods"

Tuesday, February 10

10:30 GRADUATE STUDENT SEMINAR  - Room MSC 459
      Norm Preston, Dept. of Mathematics and Statistics, BGSU. 
      "An approximation theory approach to estimating probability 
       density functions"
      Abstract: In approximation theory, a function is estimated by a
        linear combination of basis functions.  Let X_1, X_2, ..., X_n
        be a random sample taken from a probability density function
        f.  The goal of this talk is to use approximation theory to
        estimate this probability density function.

      Everybody is welcome to attend.  

 2:30 SCIENTIFIC COMPUTATION SEMINAR  - Room 459 MSC
      So-Hsiang Chou, Dept. of Mathematics and Statistics, BGSU. 
      "Linearized stability analysis for nonlinear systems"

 2:30 MAPLE WORKSHOP  - Scientific Computing Lab, MSC
      John Gresser, Dept. of Mathematics and Statistics, BGSU. 

 3:30 FACULTY MEETING  - Room 459 MSC
      Discussion of the department's hiring plans

Wednesday, February 11

11:30 MATHEMATICS EDUCATION SEMINAR  - Room 447 MSC
      Barbara Moses, Dept. of Mathematics and Statistics, BGSU. 
      "Von Glasersfeld radical constructivism"
      
Thursday, February 12

 1:00 STATISTICAL COMPUTING SEMINAR  - Room 459 MSC
      Jim Albert, Dept. of Mathematics and Statistics, BGSU. 
      "Numerical integration"

Friday, February 13
      
 3:30 Coffee
 3:45 COLLOQUIUM  - Room 459 MSC
      J. G. Wade, Dept. of Mathematics and Statistics, BGSU. 
      "Preconditioned iterative methods for regularized inverse problems"
      Abstract: We shall consider numerical methods for solving
        semidefinite least-squares formulations of illposed inverse
        problems, with total variation (TV) regularization. TV
        regularization entails adding a term to the least-squares
        objective functional which penalizes total variation of the
        solution; this term formally appears as (a scalar times) the
        L-1 norm of the gradient.

        The advantage of this regularization is that it improves the
        conditioning of the optimization problem while not
        penalizing discontinuities in the solution, which is
        important in applications. This approach has enjoyed
        significant success in image denoising and deblurring, laser
        interferometry, electrical tomography, and estimation of
        permeabilities in porous media flow models.

        The main drawback with TV regularization is that with it, the
        optimization problem becomes nonquadratic, so that
        mathematical and numerical analysis are both more involved. In
        particular, the first-order necessary condition for minimizers
        (e.g., "setting the first variation equal to zero") yields a
        nonlinear integro-partial differential equation.

        In this talk the following will be described:

        (i) least-squares inverse problems and some interesting examples,
       (ii) the importance of regularization in general and of TV
            regularization in particular, and
      (iii) the current state of numerical methodology for efficient
            treatment of these problems.

        Numerical results will be presented.