31 citations · 85 across the 24 of their papers we have counts for
5 papers · 1 filter
Rational Krylov methods for functions of matrices with applications to fractional partial differential equations
Lidia Aceto, Daniele Bertaccini, Fabio Durastante +1
In this paper, we propose a new choice of poles to define reliable rational Krylov methods. These methods are used for approximating function of positive definite matrices. In part…
On Krylov solutions to infinite-dimensional inverse linear problems
Noe Caruso, Alessandro Michelangeli, Paolo Novati
We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient co…
On general convergence behaviours of finite-dimensional approximants for abstract linear inverse problems
Noe Caruso, Alessandro Michelangeli, Paolo Novati
In the framework of abstract linear inverse problems in infinitedimensional Hilbert space we discuss generic convergence behaviours of approximate solutions determined by means of…
Rational approximations to fractional powers of self-adjoint positive operators
Lidia Aceto, Paolo Novati
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provi…
Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems
Silvia Gazzola, Silvia Noschese, Paolo Novati +1
GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as D…