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Convergence of the conjugate gradient method with unbounded operators

Show simple item record Caruso, Noe Michelangeli, Alessandro 2019-08-27T08:49:29Z 2019-08-27T08:49:29Z 2019-08-27
dc.description.abstract In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove the convergence of the conjugate gradient iterates to an exact solution to the inverse problem in the most general case where the self-adjoint, non-negative operator is unbounded and with minimal, technically unavoidable assumptions on the initial guess of the iterative algorithm. The convergence is proved to always hold in the Hilbert space norm (error convergence), as well as at other levels of regularity (energy norm, residual, etc.) depending on the regularity of the iterates. We also discuss, both analytically and through a selection of numerical tests, the main features and differences of our Convergence result as compared to the case, already available in the literature, where the operator is bounded. en_US
dc.language.iso en en_US
dc.relation.ispartofseries SISSA;20/2019/MATE
dc.subject inverse linear problems en_US
dc.subject infinite-dimensional Hilbert space en_US
dc.subject ill-posed problems en_US
dc.subject Krylov subspaces methods en_US
dc.subject conjugate gradient en_US
dc.subject self-adjoint operators en_US
dc.subject spectral measure en_US
dc.subject orthogonal polynomials en_US
dc.title Convergence of the conjugate gradient method with unbounded operators en_US

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