We consider linear least squares problems of very large dimension, such as those arising for example in inverse problems. We introduce an associated approximate problem, within a subspace spanned by a relatively small number of basis functions, and solution methods that use simulation, importance sampling, and low-dimensional calculations. The main components of this methodology are a regression/regularization approach that can deal with nearly singular problems, and an importance sampling design approach that exploits existing continuity structures in the underlying models, and allows the solution of very large problems.

Submitted to SIAM Journal of Scientific Computing 2010

The 9th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing Monte Carlo and Quasi-Monte Carlo Methods 2010, edited by Henryk Wozniakowski and Leszek Plaskota. (MCQMC 2010) will be published by Springer-Verlag, in a book entitled

Submitted to Hybrid Systems: Computation and Control (HSCC) Conference

We consider linear least squares problems of very large dimension, such as those arising for example in inverse problems. We introduce an associated approximate problem, within a subspace spanned by a relatively small number of basis functions, and solution methods that use simulation, importance sampling, and low-dimensional calculations. The main components of this methodology are a regression/regularization approach that can deal with nearly singular problems, and an importance sampling design approach that exploits existing continuity structures in the underlying models, and allows the solution of very large problems.

Submitted to SIAM Journal of Scientific Computing

Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, 2008 PP 1370-1374

Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, 2008 pp 2252-2257