### Friday, October 31

## MS12

Linear Algebra for Ill-Posed Problems and Image Processing

10:00 AM-12:00 PM

*Room: Ballroom 2 *

Many problems in science and engineering are concerned with the determination of the internal structure of a system from exterior measurements. These problems typically are ill-posed. Their discretization can give rise to large severely ill-conditioned linear or nonlinear systems of equations. The computation of a meaningful approximate solution in the presence of errors in the data requires regularization. Recently, the development of special iterative methods for determining a regularized
approximate solution of large-scale discrete ill-posed problems has received considerable attention, in particular for image processing applications. The purpose of this minisymposium to present an overview of state-of-the-art methods for the numerical solution of ill-posed problems with particular emphasis on the linear algebra involved.

**Organizer: Daniela Calvetti,**

*Stevens Institute of Technology;*

**and Lothar Reichel, **

*Kent State University*

**10:00 Efficient Algorithms for Least-squares Type Problems**
- Gene H. Golub, Stanford University
**10:30 A Regularizing Lanczos Iteration for Underdetermined Linear Systems**
- Daniela Calvetti and Lothar Reichel, Organizers; and F. Sgallari and G. Spaletta, Universita di Bologna, Italy
**11:00 Numerical Linear Algebra and Constrained Deconvolution**
*Curtis R. Vogel*, Montana State University; and James G. Nagy, Southern Methodist University
**11:30 A Modular Solver for Constrained Regularization Problems in Image Restoration**
*Tony F. Chan* and Peter Blomgren, University of California, Los Angeles

*MMD, 4/17/97*

*tjf, 6/13/97*

*MMD, 8/6/97*