Aldo Pasquali

Global Newton-type methods and semismooth reformulations for NCP

It is known that a nonlinear complementarity problem (NCP) can be reformulated as a semismooth system of nonlinear equations by using a so-called NCP-function. Global Newton-type methods for solving NCP via semismooth reformulation need to use a merit function, which is usually required to be continuously differentiable. In this paper we present a global Newton-type method which does not require the differentiability for the merit function used in the line-search procedure. The method is used to numerically compare the effectiveness of two NCP-functions widely discussed in literature, the minimum function and the Fischer-Burmeister function. The results on several examples allow to gain some new acquaintance of the respective numerical advantages of the two functions.

On real logarithms of nearby matrices and structured matrix interpolation

Theoretical and algorithmic results are given for the numerical computation of real logarithms of nearby matrices. As an application, and an original motivation for this study, interpolation for sequences of invertible matrices is considered particularly for matrices with a given structure (for example, orthogonal, symplectic, or positive definite), so that the resulting interpolants share the structural properties of the data. Error analysis, implementation details and examples are provided.

Numerical solution of unstable two-point boundary-value problems by quasilinearization and orthonormalization

This paper reports on a method of numerical solution of sensitive nonlinear two-point boundary-value problems. The method consists of a modification of the continuation technique in quasilinearization obtained by combination with an orthogonalization procedure for linear boundary-value problems.

Identification of parameters in polymer crystallization

The complex phenomenon of partial crystallization of polymers is examined. A mathematical model is exploited for the isothermal crystallization process in which the nucleation rate and the growth of the spherulites are constant. This model consists of an integro-differential equation, depending on some key parameters, whose identification is crucial for a correct description of the phenomenon. The main purpose of this work is to solve this problem numerically, using the experimental data provided by the HIMONT-ITALIA Laboratories. An error analysis of the adopted numerical method is carried out, and some numerical results are given, to show the validity and flexibility of the technique.

SOME PROPERTIES OF GMRES IN HILBERT SPACES

Our purpose in this work is to explore the properties of GMRES in Hilbert spaces. We extend to the infinite dimensional context some main results that are known to hold in the finite dimensional case. A key assumption for these extensions is that the involved linear operator is an algebraic operator.

Nonmonotone algorithms for pattern search methods

This work deals with the solution of ill-conditioned unconstrained minimization problems by means of pattern search methods. To this end, the usual requirement of monotonic reduction of the objective function is relaxed and nonmonotone pattern search methods are proposed, which maintain the convergence properties of their monotone counterparts. Numerical experimentation on several well-known ill-conditioned functions is reported. The results highlight a class of pattern search methods which benefit very much by the introduction of nonmonotone strategies.

On the convergence of nonlinear simultaneous displacements

In this work we obtain a convergence criterion for the nonlinear simultaneous displacements method. After some remarks on the iterative modified Newton-like methods, we also obtain a convergence theorem for a stationary modification of nonlinear simultaneous displacements method.

A numerical method for computing the periodic solutions of the ring-spinning balloon equations

The ring-spinning process is the last phase of the manufacturing process of textile yarn, where a loop of yarn rotates rapidly about a fixed axis and twisting occurs while the yarn is wound onto the bobbin. The surface generated by the rotating loop of the yarn is called a balloon. In this paper a numerical method is developed for the calculation of periodic solutions of a non-stationary mathematical model of the ring-spinning process recently proposed in the technical literature. Some results are given, from which the method seems to be very efficient and reliable in the simulation of realistic process.

Evaluation of a class of iterative methods for the numerical solution of Boundary value problems for ordinary differential equations

The aim of this paper is an experimental evaluation and comparison among several iterative methods proposed for approximate solution of two-point boundary value problems for ordinary differential equations.SommarioIn questa nota si presentano alcuni risultati di una analisi critica e comparativa di differenti metodi iterativi per la risoluzione approssimata di problemi ai limiti per equazioni differenziali ordinarie.

Alcune considerazioni numeriche relative alla soluzione di un noto problema ai limiti per l'equazionex=f(t,x,λ)

AbstractAn iterative method for the computation of the solution of a boundary value problem for the equation