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First-order system least-squares finite element method for singularly perturbed Darcy equations
(2023)
We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the ...
Total least squares problems on infinite dimensional spaces
(IOP Publishing, 2021-04)
We study weighted total least squares problems on infinite dimensional spaces. We present some necessary and sufficient conditions for the regularized problem to have a solution. The existence of solution can also be assured ...
Local convergence analysis of proximal Gauss-Newton method for penalized nonlinear least squares problems
We present a local convergence analysis of the proximal Gauss-Newton method for solving penalized nonlinear least squares problems in a Hilbert space setting. Using more precise majorant conditions than in earlier studies ...
Weighted Generalized Inverses, Oblique Projections, and Least-Squares Problems
(Taylor & Francis, 2005-09)
A generalization with singular weights of Moore–Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.
Arbitrary divergence speed of the least-squares method in infinite-dimensional inverse ill-posed problems
(IOP Publishing, 2006-04)
A standard engineering procedure for approximating the solutions of an infinite-dimensional inverse problem of the form Ax = y, where A is a given compact linear operator on a Hilbert space X and y is the given data, is ...