Applications of the Backus-Gilbert method to linear and some nonlinear equations
Copyright policy )Applications of the Backus-Gilbert method to linear and some nonlinear equations
We investigate the use of a functional analytical version of the Backus-Gilbert Method as a reconstruction strategy to get specific information about the solution of linear and slightly non-linear systems with Frech��t derivable operators. Some a priori error estimates are shown and tested for two classes of problems: a nonlinear moment problem and a linear elliptic Cauchy problem. For this second class of problems a special version of the Green-formula is developed in order to analyze the involved adjoint equations.
15 pages, 6 figures
Inverse problems for PDEs, Numerical solutions of ill-posed problems in abstract spaces; regularization, Numerical solutions to equations with nonlinear operators, Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs, Numerical Analysis (math.NA), Fréchet differentiable operators, noisy data, Green formula, Iterative procedures involving nonlinear operators, error estimates, Backus-Gilbert method, FOS: Mathematics, Mathematics - Numerical Analysis, nonlinear systems, 65J20, 47A52
Inverse problems for PDEs, Numerical solutions of ill-posed problems in abstract spaces; regularization, Numerical solutions to equations with nonlinear operators, Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs, Numerical Analysis (math.NA), Fréchet differentiable operators, noisy data, Green formula, Iterative procedures involving nonlinear operators, error estimates, Backus-Gilbert method, FOS: Mathematics, Mathematics - Numerical Analysis, nonlinear systems, 65J20, 47A52
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