Monday, July 14

10:30 AM-12:30 PM
Law School, Room 190

MS3
Numerical Solution of Ill-Posed Problems

Ill-posed problems are those for which small changes in the data, due, for example, to addition of noise, can cause arbitrarily large changes in the solution. The standard approach is to replace such a problem by a nearby well-posed problem. Recent research focuses on exploiting special structure in order to solve larger and harder problems. The first talk in this minisymposium concerns problems with discontinuous coefficients. The second talk considers the central issue in solution of these problems: the choice of the nearby well-posed problem. The last two speakers exploit near-Kronecker product structure or Cauchy-like structure in the ill-posed operator.

Organizer: Dianne P. O'Leary
University of Maryland, College Park

10:30 Augmented Lagrangian and Total Variation Methods For Recovery of Discontinuous Coefficients From Elliptic Equations

Tony F. Chan , University of California, Los Angeles; and Xue-Cheng Tai, University of Bergen, Norway

11:00 Regularization of Ill-Posed Problems by Envelope Guided Conjugate Gradients

Linda Kaufman, Bell Laboratories, Lucent Technologies; and Arnold Neumaier, Universitaet Wien, Austria

11:30 Kronecker Product Approximations for Large-Scale Problems in Image Restoration

James G. Nagy, Southern Methodist University

12:00 Cauchy-Like Block Diagonal Preconditioners for Ill-Posed Problems

Misha Elena Kilmer, University of Maryland, College Park; and Dianne P. O'Leary, Organizer

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