Compositional Space Parameterization Methods for Thermal.
Dr. Jack Poulson defended his dissertation on fast, distributed-memory quasi-direct solvers for heterogeneous 3D time-harmonic wave equations in 2012. He spent a brief postdoc in Stanford's math department focusing on fast, distributed-memory algorithms for applying Egorov operators and inverting so-called strongly-admissible H-matrices before.I would like to thank my collaborators Jack Poulson and Haizhao Yang for being great teachers and constant supporters. I would also like to thank my other col-laborators: Kenneth Ho, Lin Lin, Michael Mahoney, Eileen Martin, Victor Minden, Ruoxi Wang, and Liming Zhang. Without their help, my achievements would not be possible.The Mathematics Genealogy Project is in need of funds to help pay for student help and other associated costs. If you would like to contribute, please donate online using credit card or bank transfer or mail your tax-deductible contribution to: Mathematics Genealogy Project Department of Mathematics North Dakota State University P. O. Box 6050.
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. This dissertation extends the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal.The main contribution of this dissertation is the introduction of an efficient parallel sweeping preconditioner and its subsequent application to several challenging velocity models. For instance, 3D seismic problems approaching a billion degrees of freedom have been solved in just a few minutes using several thousand processors.
EFFICIENT SOLUTIONS TO TOEPLITZ-STRUCTURED LINEAR SYSTEMS FOR SIGNAL PROCESSING Approved by: Dr. James McClellan, Committee Chair School of Electrical and Computer Engineering Geo.
