Abstract
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.
Highlights
IntroductionThe first new result is a convergence proof of the algorithm to approximate a solution to a nonlinear least square problem
The paper is a continuation of the work in White (2011)
The first new result is a convergence proof of the algorithm to approximate a solution to a nonlinear least square problem
Summary
The first new result is a convergence proof of the algorithm to approximate a solution to a nonlinear least square problem. A convergence proof is given for the algorithm to approximate the solution of a coupled nonlinear algebraic system and a nonnegative least squares problem, see lines (9–11) in this paper and in White (2011). These discrete models evolve from the continuous models using the ABOUT THE AUTHOR. The most recent work is on hazard identification given observation data. The second edition of Computational Mathematics: Models, Methods and Analysis with MATLAB and MPI will be published in the fall of 2015 by CRC Press/Taylor and Francis
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