# Francesca MazziaUniversità degli Studi di Bari Aldo Moro | Università di Bari · Department of Computer Science

Francesca Mazzia

Scienze dell'Informazione / Computer Science

## About

133

Publications

22,200

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,818

Citations

Citations since 2016

Introduction

Research interest:
Numerical methods for Ordinary Differential Equations (IVP and BVP), linear and nonlinear stability properties, parallel implementation.
Numerical solution of differential algebraic equations, volterra integro-differential equations
Stability and conditioning of linear systems.
Parallel algorithms for the numerical solution of large linear systems.
testset for ivp solvers: http://www.dm.uniba.it/~testset

Additional affiliations

September 2001 - present

January 2001 - present

**Università degli Studi di Bari Aldo Moro**

Position

- TestSet for IVP solvers

September 1990 - September 2001

## Publications

Publications (133)

This paper presents new hybrid mesh selection strategies for boundary value problems implemented in the code TOM. Originally the code was proposed for the numerical solution of stiff or singularly perturbed problems. The code has been now improved with the introduction of three classes of mesh selection strategies, that can be used for different ca...

The library QIBSH++ is a C++ object oriented library for the solution of Quasi Interpolation problems. The library is based on a Hermite Quasi Interpolating operator, which was derived as continuous extensions of linear multistep methods applied for the numerical solution of Boundary Value Problems for Ordinary Differential Equations. The library i...

A point cloud describing a railway environment is considered in a case study aimed at presenting a workflow for the automatic detection of external objects that, coming too close to the railway infrastructure, may cause potential risks for its correct functioning. The approach combines classical semantic segmentation methodologies with a novel geom...

In this article, we present a new strategy to determine an unmanned aerial vehicle trajectory that minimizes its flight time in presence of avoidance areas and obstacles. The method combines classical results from optimal control theory, i.e. the Euler-Lagrange Theorem and the Pontryagin Minimum Principle, with a continuation technique that dynamic...

This research paper is concerned with developing, analyzing, and implementing an adaptive optimized one-step block Nyström method for solving second-order initial value problems of ODEs and time-dependent partial differential equations. The new technique is developed through a collocation method with a new approach for selecting the collocation poi...

In this article the authors introduce a spline Hermite quasi-interpolation technique for the preprocessing operations of imputation and smoothing of univariate time series. The constructed model is then applied for the forecast and for the anomaly detection. In particular, for the latter case, algorithms based on the combination of quasi-interpolat...

Saliency detection mimics the natural visual attention mechanism that identifies an imagery region to be salient when it attracts visual attention more than the background. This image analysis task covers many important applications in several fields such as military science, ocean research, resources exploration, disaster and land-use monitoring t...

Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontryagin’s minimum principle that generates Hamiltonian Boundary Value Problems (BVPs). In this paper, we review some general-purpose codes for the solution of BVPs and...

Current UAV technology has led to an exponential growth in the potential applications of drones in both the military and the civilian fields. Therefore, drone missions must be subject to regulations that ensure safety in operations, especially in Urban Air Mobility tasks. Nevertheless, unpredictable conditions may lead drones to dangerous routes, e...

The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting from the multi-derivative extension of the midpoint method we have obtained a new symmetric implicit Runge–Kutta method of order four, for the numerical solution of f...

These slides summarize the results published in the paper "Novel Reconstruction Errors for Saliency Detection in Hyperspectral Images".

When hyperspectral images are analyzed, a big amount of data, representing the reflectance at hundreds of wavelengths, needs to be processed. Hence, dimensionality reduction techniques are used to discard unnecessary information. In order to detect the so called “saliency”, i.e., the relevant pixels, we propose a bottom-up approach based on three m...

We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can handle both infinite and infinitesimal quantities expressed using the positive and negative finite or infinite pow...

Saliency detection extracts objects attractive to a human vision system from an image. Although saliency detection methodologies were originally investigated on RGB color images, recent developments in imaging technologies have aroused the interest in saliency detection methodologies for data captured with high spectral resolution using multispectr...

In this paper, we deal with the computation of Lie derivatives, which are required, for example, in some numerical methods for the solution of differential equations. One common way for computing them is to use symbolic computation. Computer algebra software, however, might fail if the function is complicated, and cannot be even performed if an exp...

We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can handle both infinite and infinitesimal quantities symbolized by the positive and negative finite powers of the rad...

We introduce a dynamic precision floating-point arithmetic based on the Infinity Computer. This latter is a computational platform which can handle both infinite and infinitesimal quantities epitomized by the positive and negative finite powers of the symbol Open image in new window, which acts as a radix in a corresponding positional numeral syste...

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known Lane-Emden equation, albeit under boundary conditions that differ from those usually assumed in the astrophysica...

The energy transfer among the components in a gas determines its fate. Especially at low temperatures, inelastic collisions drive the cooling and the heating mechanisms. In the early Universe as well as in zero- or low- metallicity environments the major contribution comes from the collisions among atomic and molecular hydrogen, also in its deutera...

The energy transfer among the components in a gas determines its fate. Especially at low temperatures, inelastic collisions drive the cooling and the heating mechanisms. In the early Universe as well as in zero-or low-metallicity environments the major contribution comes from the collisions among atomic and molecular hydrogen, also in its deuterate...

We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the...

Multi-derivative one-step methods based upon Euler–Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any multi-derivative Runge–Kutta methods, we show that the Euler–MacLaurin method of order p is conjugate-symplectic up to...

The authors of the above mentioned paper specify that the considered class of one-step symmetric Hermite-Obreshkov methods satisfies the property of conjugate-symplecticity up to order p + r , where r = 2 and p is the order of the method. This generalization of conjugate-symplecticity states that the methods conserve quadratic first integrals and t...

We open the paper with introductory considerations describing the motivations of our long-term research plan targeting gravitomagnetism, illustrating the fluid-dynamics numerical test case selected for that purpose, that is, a perfect-gas sphere contained in a solid shell located in empty space sufficiently away from other masses, and defining the...

In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with...

The class of A-stable symmetric one-step Hermite–Obreshkov (HO) methods introduced by F. Loscalzo in 1968 for dealing with initial value problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order...

Multi-derivative one-step methods based upon Euler-Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any multi-derivative Runge-Kutta methods, we show that Euler-MacLaurin formulae are all topologically conjugate to a sympl...

In this note we consider the use of Euler–Maclaurin methods for the solution of canonical Hamiltonian problems. As a subclass of multi-derivative Runge–Kutta methods, these integrators cannot be symplectic, however they turn out to be conjugate symplectic. The numerical solutions provided by a conjugate symplectic integrator essentially share the s...

The class of A-stable symmetric one-step Hermite-Obrechkoff (HO) methods introduced in [1] for dealing with Initial Value Problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are co...

We propose a model-based method that allows to estimate the magnetic force accurately, hence the armature displacement of linear solenoids. The nonlinear electrodynamical model of solenoids is used. The unscented Kalman filter is applied to analyze the current transient response, and the dynamics of the solenoid is estimated at each time instant. F...

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial conditions are proposed. They are designed for working on a new kind of a supercomputer – the Infinity Computer – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to cal...

Magnetic particle imaging (MPI) is a new medical imaging technique capable of recovering the distribution of superparamagnetic particles from their measured induced signals. In literature there are two main MPI reconstruction techniques: measurement-based (MB) and x-space (XS). The MB method is expensive because it requires a long calibration proce...

A well-known drawback of algorithms based on Taylor series formulae is that the explicit calculation of higher order derivatives formally is an over-elaborate task. To avoid the analytical computation of the successive derivatives, numeric and automatic differentiation are usually used. A recent alternative to these techniques is based on the calcu...

Spline quasi-interpolation (QI) is a general and powerful approach for the
construction of low cost and accurate approximations of a given function. In
order to provide an efficient adaptive approximation scheme in the bivariate
setting, we consider quasi-interpolation in hierarchical spline spaces. In
particular, we study and experiment the featur...

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calcul...

The paper introduces a new class of consensus protocols to reach an agreement in networks of agents with discrete time dynamics. In order to guarantee the convergence of the proposed algorithms, some general results are proved in the framework of non-negative matrix theory. Moreover, we characterize the set of the consensus protocols and we specify...

A new class of Linear Multistep Methods based on B-splines for the numerical solution of semi-linear second order Boundary Value Problems is introduced. The presented schemes are called BS2 methods, because they are connected to the BS (B-spline) methods previously introduced in the literature to deal with first order problems. We show that, when u...

In this paper, we develop a new mesh selection strategy based on the computation of some conditioning parameters which allows to give information about the conditioning and the stiffness of the problem. The reliability of the proposed algorithm is demonstrated by some numerical experiments. We observe that “when an initial value problem is run on a...

Conference code: 111492, Export Date: 24 September 2015, References: Ascher, U.M., Christiansen, J., Russell, R.D., Collocation software for boundary-value (1981) ODEs. Acm Trans. Math Software, 7, pp. 209-222;

Magnetic particle imaging (MPI) is a new medical imaging technique capable of recovering the distribution of superparamagnetic particles from their measured induced signals [1]. In literature there are two main MPI reconstruction techniques: measurement-based (MB) and x-space (XS). In the first approach the unknown magnetic particles concentration...

In this article, block BS methods are considered for the numerical solution of Volterra integro-differential equations (VIDEs). Convergence and stability properties are analyzed. A new Matlab code for the solution of VIDEs, called VIDEBS, is presented. Numerical results using a variable stepsize implementation show the effectiveness of the proposed...

The R package bvpSolve for the numerical solution of boundary value problems (BVPs) is presented. This package is free software which is distributed under the GNU General Public License, as part of the R open source software project. It includes some well known codes to solve boundary value problems of ordinary differential equations and differenti...

We present some numerical experiments with the Matlab code TOMG, based
on symmetric block Boundary Value Methods, a class of methods for which
experiments have shown that the numerical solution nearly-preserve some
type of invariants over long-time integration.

In this article we describe the code bvptwp.m, a MATLAB code for the solution of two point boundary value problems. This code is based on the well-known Fortran codes, twpbvp.f, twpbvpl.f and acdc.f, that employ a mesh selection strategy based on the estimation of the local error, and on revisions of these codes, called twpbvpc.f, twpbvplc.f and ac...

In this paper, we introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. We rigorously prove that these schemes ...

In this paper we present the R package deTestSet that includes challenging test problems written as ordinary differential equations (ODEs), differential algebraic equations (DAEs) of index up to 3 and implicit differential equations (IDEs). In addition it includes 6 new codes to solve initial value problems (IVPs). The R package is derived from the...

Two new classes of quadrature formulas associated to the BS Boundary Value Methods are discussed. The first is of Lagrange type and is obtained by directly applying the BS methods to the integration problem formulated as a (special) Cauchy problem. The second descends from the related BS Hermite quasi-interpolation approach which produces a spline...

Numerous examples help the reader to quickly solve a variety of differential equations in the open source software R
Shows how R can be used as a problem solving environment, using examples from the biological, chemical, physical, mathematical sciences
Introduces the theory behind solution methods of differential equations at a basic level
Mathemat...

In the previous chapter we derived a simple finite difference method, namely the explicit Euler method, and we indicated how this can be analysed so that we can make statements concerning its stability and order of accuracy. If Euler’s method is used with constant time step h then it is convergent with an error of order O(h) for all sufficiently sm...

Differential equations (DEs) occur in many branches of science and technology, and there is a real need to solve them both accurately and efficiently. There are relatively few problems for which an analytic solution can be found, so if we want to solve a large class of problems, then we need to resort to numerical calculations. In this chapter we w...

When solving initial value problems for ordinary differential equations, differential algebraic equations or partial differential equations, as discussed in previous chapters, a unique solution to the equations, if it exists, is obtained by specifying the values of all the components at the starting point of the range of integration. With boundary...

Boundary Value Problems can be solved in R using shooting, MIRK and collocation methods and these can be found in the R package bvpSolve. The functions in this R package have an interface which is similar to the interface of the initial value problem solvers in the package deSolve. The default input to the solvers is very simple, requiring specific...

In Chaps. 2 and 3 we were concerned mainly with the numerical solution of ordinary differential equations of the form y′ = f(x, y). However, there are problems which are more general than this and require special methods for their solution. One such class of problems are differential algebraic equations (DAEs). An important class of DAEs are those...

Both Runge-Kutta and linear multistep methods are available to solve initial value problems for ordinary differential equations in the R packages deSolve and deTestSet. Nearly all of these solvers use adaptive step size control, some also control the order of the formula adaptively, or switch between different types of methods, depending on the loc...

A characteristic of partial differential equations (PDEs) is that the solution changes as a function of more than one independent variable. Usually these variables are time and one or more spatial coordinates. The numerical solution of a PDE therefore often requires the solution to be approximated not only in time as in ODEs, but in space as well....

R contains several methods for the solution of initial value problems for DAEs, which are embedded in the R packages deSolve and deTestset. Four of these, based on RADAU5, MEBDF, block implicit or Adams methods, can solve DAEs of index up to three written in Hessenberg form. The fifth method, based on BDF, is very efficient for index 1 problems and...

R has three packages that are useful for solving partial differential equations. The R package ReacTran offers grid generation routines and the discretization of the advective-diffusive transport terms on these grids. In this way, the PDEs are either rewritten as a set of ODEs or as a set of algebraic equations. When solving the PDEs with the metho...

In this paper we will be concerned with numerical methods for the solution of nonlinear systems of two point boundary value
problems in ordinary differential equations. In particular we will consider the question “which codes are currently available
for solving these problems and which of these codes might we consider as being state of the art”. In...

This paper describes a new practical strategy to detect stiffness based on explicit Runge-Kutta schemes. This strategy implements an operative definition of stiffness based on the computation of two conditioning parameters. Test results, using a modified version of the MATLAB code DOPRI5, indicate that the new strategy is able to detect whether a p...

This document implements several testproblems that can be found on http://www.ma. ic.ac.uk/~jcash/BVP_software/PROBLEMS.PDF, using solvers from package bvpSolve (Soetaert, Cash, and Mazzia 2009a).

Almost all the difficult mathematical problems arising in the applications are solved numerically. This is especially true for large size linear problems and for nonlinear ones. The main tools for the numerical treatment of problems on computers are appropriate codes which are highly sophisticated programs, able to solve specific classes of mathema...

The notion of stiffness, which originated in several applications of a
different nature, has dominated the activities related to the numerical
treatment of differential problems for the last fifty years. Contrary to what
usually happens in Mathematics, its definition has been, for a long time, not
formally precise (actually, there are too many of t...

The notion of stiffness, which originated in several applications of different nature, has dominated the activities related to the numerical treatment of differential problems in the last fifty years. Its definition has been, for a long time, not formally precise. The needs of applications, especially those rising in the construction of robust and...

The BS Hermite spline quasi-interpolation scheme is presented. It is related to the continuous extension of the BS linear
multistep methods, a class of Boundary Value Methods for the solution of Ordinary Differential Equations. In the ODE context,
using the numerical solution and the associated numerical derivative produced by the BS methods, it is...

The computation of consistent initial values is one of the basic problems when solving initial or boundary value problems
of DAEs. For a given DAE it is, in fact, not obvious how to formulate the initial conditions that lead to a uniquely solvable
IVP. The existing algorithms for the solution of this problem are either designed for fixed index, or...

B-spline methods are Linear Multistep Methods based on B-splines which have good stability properties [F. Mazzia, A. Sestini, D. Trigiante, B-spline multistep methods and their continuous extensions, SIAM J. Numer Anal. 44 (5) (2006) 1954–1973] when used as Boundary Value Methods [L. Brugnano, D. Trigiante, Convergence and stability of boundary val...