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In the framework of iterative regularization techniques for large-scale linear ill-posed problems, this paper introduces a novel algorithm for the choice of the regularization parameter when performing the Arnoldi–Tikhonov method. Assuming that we can apply the discrepancy principle, this new strategy can work without restrictions on the choice of the regularization matrix. Moreover, this method is also employed as a procedure to detect the noise level whenever it is just overestimated. Numerical experiments arising from the discretization of integral equations and image restoration are presented

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In this paper we analyze the convergence of some commonly used Krylov subspace methods for computing the action of matrix Mittag-Leffler functions. As it is well known, such functions find application in the solution of fractional differential equations. We illustrate the theoretical results by some numerical experiments.

In this paper we introduce a method for the approximation of the matrix exponential obtained by interpolation in zeros of Faber polynomials. In particular, we relate this computation to the solution of linear IVPs. Numerical examples arising from practical problems are examined