31 citations · 135 across the 13 of their papers we have counts for
13 papers
Efficient computation of the sinc matrix function for the integration of second-order differential equations
Lidia Aceto, Fabio Durastante
This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differe…
Theoretical error estimates for computing the matrix logarithm by Padé-type approximants
Lidia Aceto, Fabio Durastante
In this article, we focus on the error that is committed when computing the matrix logarithm using the Gauss--Legendre quadrature rules. These formulas can be interpreted as Padé a…
Efficient computation of the Wright function and its applications to fractional diffusion-wave equations
Lidia Aceto, Fabio Durastante
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. T…
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…
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…
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…
Matrix approach to hypercomplex Appell polynomials
Lidia Aceto, Helmuth Robert Malonek, Graça Tomaz
Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to co…
A unified matrix approach to the representation of Appell polynomials
Lidia Aceto, Helmuth R. Malonek, Graça Tomaz
In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix - a special matrix whi…
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…
Matrix methods for radial Schrödinger eigenproblems defined on a semi-infinite domain
Lidia Aceto, Cecilia Magherini, Ewa B. Weinmüller
In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schrödinger equation posed on a semi-infinite interval. The original problem is f…