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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 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…