Convergence of the conjugate gradient method with unbounded operators

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dc.contributor.authorCaruso, Noe
dc.contributor.authorMichelangeli, Alessandro
dc.date.accessioned2019-08-27T08:49:29Z
dc.date.available2019-08-27T08:49:29Z
dc.date.issued2019-08-27
dc.description.abstractIn 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.identifier.urihttps://openscience.sissa.it/handle/1963/35338
dc.language.isoenen_US
dc.relation.ispartofseriesSISSA;20/2019/MATE
dc.subjectinverse linear problemsen_US
dc.subjectinfinite-dimensional Hilbert spaceen_US
dc.subjectill-posed problemsen_US
dc.subjectKrylov subspaces methodsen_US
dc.subjectconjugate gradienten_US
dc.subjectself-adjoint operatorsen_US
dc.subjectspectral measureen_US
dc.subjectorthogonal polynomialsen_US
dc.titleConvergence of the conjugate gradient method with unbounded operatorsen_US
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