| Título: | Arbitrary Divergence Speed of the Least-Squares Method in Infinite-Dimensional Inverse Ill-Posed Problems |
| Autores: |
Ruben D. Spies; Instituto de Matemática Aplicada del Litoral, IMAL, CONICET-UNL Karina G. Temperini; Instituto de Matemática Aplicada del Litoral, IMAL, CONICET-UNL |
| Fecha: | 2010-06-07 |
| Publicador: | Cuadernos de Matemática y Mecánica |
| Fuente: |
 |
| Tipo: |
Articles |
| Tema: | No aplica |
| Descripción: | 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 to find a sequence {XN} of finite-dimensional approximating subspaces of X whose union is dense in X and to construct the sequence {xN} of least squares solutions of the problem in XN. In 1980, Seidman (Nonconvergence Results for the Application of Least-Squares Estimation to Ill-Posed Problems, Journal of Optimization Theory and Applications, 30, 4, 535-547, 1980) showed that if the problem is ill-posed, then, without any additional assumptions on the exact solution or on the sequence of approximating subspaces {XN}, it cannot be guaranteed that the sequence fxNg will converge to the exact solution. In this article this result is extended in the following sense: it is shown that if X is separable, then for any y in X, y not equal 0, and for any arbitrarily given function s defined over the natural numbers with values in R+, there exists an injective, compact linear operator A and an increasing sequence of finite-dimensional subspaces XN contained in X such that ||xN - A^{-1}y||>= s(N) for all N, where xN is the least squares solution of Ax = y in XN. |
| Idioma: | Inglés |
1 Sloshing in a Multi-Physics Parallel Programming Paradigm por Laura Battaglia; CIMEC-INTEC-CONICET-UNL,Jorge D'Elía; CIMEC-INTEC-CONICET-UNL,Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL,Norberto Marcelo Nigro; CIMEC-INTEC-CONICET-UNL | 6 MPI for Python por Lisandro Daniel Dalcín; CIMEC-INTEC-CONICET-UNL,Rodrigo Rafael Paz; CIMEC-INTEC-CONICET-UNL,Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL |
2 A Minimal Element Distortion Strategy for Computational Mesh Dynamics por Ezequiel López; CIMEC-INTEC-CONICET-UNL,Norberto Marcelo Nigro; CIMEC-INTEC-CONICET-UNL,Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL,Jorge Toth; Universidad Nacional del Comahue | 7 An interface strip preconditioner for domain decomposition methods: Application to hydrology por Rodrigo Rafael Paz; CIMEC-INTEC-CONICET-UNL,Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL |
3 Strong coupling strategy for fluid structure interaction problems in supersonic regime via fixed point iteration por Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL,Norberto Marcelo Nigro; CIMEC-INTEC-CONICET-UNL,Rodrigo Rafael Paz; CIMEC-INTEC-CONICET-UNL | 8 A Preconditioner for the Schur Complement Matrix por Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL,Lisandro Daniel Dalcín; CIMEC-INTEC-CONICET-UNL,Rodrigo R. Paz; CIMEC-INTEC-CONICET-UNL,Andrea Yommi; CIMEC-INTEC-CONICET-UNL,Victorio E. Sonzogni; CIMEC-INTEC-CONICET-UNL,Norberto M. Nigro; CIMEC-INTEC-CONICET-UNL |
4 Hot-pressing process modeling for medium density fiberboard (MDF) por Norberto Marcelo Nigro; CIMEC-INTEC-CONICET-UNL,Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL | 9 Finite Element Methods for Surface Diffusion por Eberhard Bansch,Pedro Morin; IMAL-CONICET-UNL,Ricardo Nochetto |
5 On the efficiency and quality of numerical solutions in CFD problems using the Interface Strip Preconditioner for domain decomposition methods por Rodrigo Rafael Paz; CIMEC-INTEC-CONICET-UNL,Norberto Marcelo Nigro; CIMEC-INTEC-CONICET-UNL,Mario Alberto Storti; CIMEC-INTEC-CONICET-UNL | 10 A finite element method for surface diffusion: the parametric case por Pedro Morin; IMAL-CONICET-UNL,Eberhard Bänsch,Ricardo H. Nochetto |