31 citations · 68 across the 15 of their papers we have counts for
16 papers
A Multi-Order Extension of Fractional HBVMs (FHBVMs)
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
The efficient numerical solution of fractional differential equations has been recently tackled through the definition of Fractional HBVMs (FHBVMs), a class of Runge-Kutta type met…
Analysis and implementation of collocation methods for fractional differential equations
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
Recently, the class of Runge-Kutta type methods named Fractional HBVMs (FHBVMs) has been introduced for the numerical solution of initial value problems of fractional differential…
Solving FDE-IVPs by using Fractional HBVMs: some experiments with the fhbvm code
L. Brugnano, G. Gurioli, F. Iavernaro
In this paper we report a few numerical tests by using a slight extension of the Matlab code fhbvm in [8], implementing Fractional HBVMs, a recently introduced class of numerical m…
Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments
Gianmarco Gurioli, Weijie Wang, Xiaoqiang Yan
In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems…
Numerical solution of FDE-IVPs by using Fractional HBVMs: the fhbvm code
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro
In this paper we describe the efficient numerical implementation of Fractional HBVMs, a class of methods recently introduced for solving systems of fractional differential equation…
A shooting-Newton procedure for solving fractional terminal value problems
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro
In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is parti…
Trust-region algorithms: probabilistic complexity and intrinsic noise with applications to subsampling techniques
S. Bellavia, G. Gurioli, B. Morini +1
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown tha…
The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini +1
Intrinsic noise in objective function and derivatives evaluations may cause premature termination of optimization algorithms. Evaluation complexity bounds taking this situation int…
Quadratic and Cubic Regularisation Methods with Inexact function and Random Derivatives for Finite-Sum Minimisation
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini +1
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant p…
Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives
S. Bellavia, G. Gurioli, B. Morini +1
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unco…
Stochastic Analysis of an Adaptive Cubic Regularisation Method under Inexact Gradient Evaluations and Dynamic Hessian Accuracy
Stefania Bellavia, Gianmarco Gurioli
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisat…
Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization
S. Bellavia, G. Gurioli, B. Morini +1
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained p…
Adaptive Cubic Regularization Methods with Dynamic Inexact Hessian Information and Applications to Finite-Sum Minimization
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini
We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynam…
Spectrally Accurate Energy-preserving Methods for the Numerical Solution of the "Good" Boussinesq Equation
Luigi Brugnano, Gianmarco Gurioli, Chengjian Zhang
In this paper we study the geometric solution of the so called "good" Boussinesq equation. This goal is achieved by using a convenient space semi-discretization, able to preserve t…
Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro
In this paper we are concerned with the analysis of a class of geometric integrators, at first devised in [14, 18], which can be regarded as an energy-conserving variant of Gauss c…
Line Integral Solution of Hamiltonian Systems with Holonomic Constraints
Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro +1
In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the…