Robert White
North Carolina State University
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Featured researches published by Robert White.
SIAM Journal on Matrix Analysis and Applications | 1989
Robert White
Parallel algorithms generated by multisplittings are considered. A parallel algorithm may be formed, first, by concurrently executing the iteration associated with each splitting, and second, by forming a weighted sum of these computations. However, it is not imperative that the weighting be done last. Convergence results are obtained for a variety of other weighting schemes. In particular, it is shown that preweighting is in some cases more desirable than the traditional postweighting. Furthermore, we indicate how one can use a symmetric weighting scheme to obtain a good multisplitting version of the SSOR preconditioner. These algorithms are illustrated by computations done on an Alliant
International Journal of Computer Mathematics | 2009
Robert White
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International Journal of Computer Mathematics | 2011
Robert White
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Cogent Mathematics | 2015
Robert White
This paper is a numerical study of populations with dispersion (Fickian diffusion) in one or two directions and with a finite number of impulsive culling sites. The intensities and locations of the culling sites are used for optimal control of the population density. The identifications of the model parameters and location of the culling sites are determined from the given population density data. The Levenberg–Marquardt, variation of the simulated-annealing and semilinear-SOR algorithms are used.
SIAM Journal on Matrix Analysis and Applications | 2000
Robert White
Given some observations downstream can one determine the location and intensities of point sources of a hazard (pollutant chemical or biological)? The unknown concentrations are governed by the diffusion-advection partial differential equation. The corresponding algebraic system is studied. The fixed location problem is considered using reordering, the Schur complement and nonnegative least squares. A nonlinear problem is proposed, and an iterative method is formulated based on nonnegative least squares and Newtons method. The variable location problem is tackled with simulated annealing. The complexities of controlling aquatic populations, which are nonlinear, time-dependent and have multiple sources, will be illustrated.
Archive | 2004
Robert White
Given observations of selected concentrations one wishes to determine unknown intensities and locations of the sources for a hazard. The concentration of the hazard is governed by a steady-state nonlinear diffusion–advection partial differential equation and the best fit of the data. The discretized version leads to a coupled nonlinear algebraic system and a nonlinear least squares problem. The coefficient matrix is a nonsingular M-matrix and is not symmetric. Iterative methods are compositions of nonnegative least squares and Picard/Newton methods, and a convergence proof is given. The singular values of the associated least squares matrix are important in the convergence proof, the sensitivity to the parameters of the model, and the location of the observation sites.
Archive | 2003
Robert White
Consider a linear algebraic problem where the set of unknowns is a union of subsets. Let the coefficient matrix have a splitting associated with each subset. The traditional multisplitting method forms a weighted sum, over the overlapping unknowns, of the iterates for each such splitting to obtain a single parallel iterative method. An optimal alternative to the weighted sums will be presented. Convergence of this new form of multisplitting (MS) method can be studied for both symmetric positive definite (SPD) matrices and M-matrices. Applications to PDEs and the equilibrium equations for fluid flow in a driven cavity will be presented.
Archive | 2003
Robert White
Archive | 2003
Robert White
Archive | 2003
Robert White