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This paper introduces two new algorithms, belonging to the class of Arnoldi-Tikhonov regularization methods, which are particularly appropriate for sparse reconstruction. The main idea is to consider suitable adaptively-defined regularization matrices that allow the usual 2-norm regularization term to approximate a more general regularization term expressed… (More)

SUMMARY This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right-hand side is assumed; an… (More)

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