31 citations · 85 across the 24 of their papers we have counts for
25 papers
A simple algorithm for the summation of alternating series
Eleonora Denich, Paolo Novati, Alvise Sommariva
This paper deals with the computation of the sum of alternating series, whose general terms can be expressed by means of analytic functions. After rewriting the series as a weighte…
On modified anti-Gaussian rules for Jacobi weight functions
Eleonora Denich, Paolo Novati, Alvise Sommariva
Anti-Gaussian formulas represent an efficient tool for a dynamical estimation of the error of the underlying Gaussian rule. When applied to the Jacobi weight function it is known t…
A general class of iterative splitting methods for solving linear systems
Paolo Novati, Fulvio Tagliaferro, Marino Zennaro
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict di…
Some notes on the trapezoidal rule for Fourier type integrals
Eleonora Denich, Paolo Novati
This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows t…
A fast and simple algorithm for the computation of the Lerch transcendent
Eleonora Denich, Paolo Novati
This paper deals with the computation of the Lerch transcendent by means of the Gauss-Laguerre formula. An a priori estimate of the quadrature error, that allows to compute the num…
A fast and accurate numerical approach for electromagnetic inversion
Eleonora Denich, Paolo Novati, Stefano Picotti
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximate…
A Gauss Laguerre approach for the resolvent of fractional powers
Eleonora Denich, Laura Grazia Dolce, Paolo Novati
This paper introduces a very fast method for the computation of the resolvent of fractional powers of operators. The analysis is kept in the continuous setting of (potentially unbo…
A Gaussian method for the operator square root
Eleonora Denich, Paolo Novati
We consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. The approximation is of rational type and comes from the use of the Gau…
Gaussian rule for integrals involving Bessel functions
Eleonora Denich, Paolo Novati
In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation…
Exponentially convergent trapezoidal rules to approximate fractional powers of operators
Lidia Aceto, Paolo Novati
In this paper we are interested in the approximation of fractional powers of self-adjoint positive operators. Starting from the integral representation of the operators, we apply t…
Fast and accurate approximations to fractional powers of operators
Lidia Aceto, Paolo Novati
In this paper we consider some rational approximations to the fractional powers of self-adjoint positive operators, arising from the Gauss-Laguerre rules. We derive practical error…
Padé-type approximations to the resolvent of fractional powers of operators
Lidia Aceto, Paolo Novati
We study a reliable pole selection for the rational approximation of the resolvent of fractional powers of operators in both the finite and infinite dimensional setting. The analys…
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…
Some transpose-free CG-like solvers for nonsymmetric ill-posed problems
Silvia Gazzola, Paolo Novati
This paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov so…
Rational approximation to the fractional Laplacian operator in reaction-diffusion problems
Lidia Aceto, Paolo Novati
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the…
On the construction of -step methods for FDEs
Lidia Aceto, Cecilia Magherini, Paolo Novati
In this paper we consider the numerical solution of Fractional Differential Equations by means of -step recursions. The construction of such formulas can be obtained in many way…
Embedded techniques for choosing the parameter in Tikhonov regularization
Silvia Gazzola, Paolo Novati, Maria Rosaria Russo
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. T…
A GCV based Arnoldi-Tikhonov regularization method
Paolo Novati, Maria Rosaria Russo
For the solution of linear discrete ill-posed problems, in this paper we consider the Arnoldi-Tikhonov method coupled with the Generalized Cross Validation for the computation of t…
Using the RD rational Arnoldi method for exponential integrators
Paolo Novati
In this paper we investigate some practical aspects concerning the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of expon…
Preconditioning linear systems via matrix function evaluation
Paolo Novati, Michela Redivo-Zaglia, Maria Rosaria Russo
For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method…