Browsing by Author "Capcelea, Titu"

Now showing 1 - 10 of 10

ALGORITHM FOR THE LOCALIZATION OF SINGULARITIES OF FUNCTIONS DEFINED ON CLOSED CONTOURS
(CEP USM, 2017) Capcelea, Maria; Capcelea, Titu
A numerical algorithm for locating polar singularities of functions defined on a discrete set of points of a simple closed contour in the complex plane is examined. The algorithm uses the Faber-Pad ́e approximation of the function and the fact that the zeros of its denominator give us approximations of the poles of function. The numerical performance of the algorithm is being analyzed on test issues.
ALGORITM EFECTIV PENTRU REZOLVAREA ECUAŢIILOR INTEGRALE SINGULARE
(CEP USM, 2007) Capcelea, Titu
We present a fast algorithm with O(n log n) computational complexity for the approximate solution of Cauchy 2 singular integral equations with smooth continuous coefficients, defined on the unit circle of the complex plane. In order to obtain this algorithm we adopt Amosov`s idea [1] to the quadrature method. In the case when the approximate method is applicable [2], the solution ϕn of the mentioned fast algorithm satisfies the same convergence rate as the solution n ∗ ϕ of the quadrature method.
ALGORITM PENTRU DETERMINAREA STRATEGIILOR OPTIME STAŢIONARE ÎNPROBLEMELE STOCASTICE DE CONTROL OPTIMAL DISCRET PE REŢELE DECIZIONALE CU MULTIPLE CLASE RECURENTE
(CEP USM, 2015) Capcelea, Maria; Capcelea, Titu
Este elaborat şi argumentat teoretic un algoritm eficient pentru determinarea strategiilor optime staţionare în problemele stocastice de control optimal discret cu perioada de dirijare infinită, definite pe reţele decizionale cu multiple clase recurente, în care este aplicat criteriul de optimizare a combinaţiei convexe a costurilor medii în clasele recurente. Sunt examinate probleme în care costurile de tranziţie între stările sistemului dinamic şi probabilităţile de tranziţie, definite în stările necontrolabile, sunt constante independente de timp. Algoritmul elaborat este bazat pe modelul de programare liniară pentru determinarea strategiilor optime în problemele de control definite pe reţele decizionale perfecte [3,4].
ALGORITMI EFICIEN Ţ I PENTRU REZOLVAREA SISTEMELOR DE ECUAŢII CE APAR LA DISCRETIZAREA ECUAŢIILOR INTEGRALE SINGULARE
(CEP USM, 2008) Capcelea, Maria; Capcelea, Titu; Lazari, Alexandru
It is marked out the class of iterative algorithms for solvin g of systems of equations which are obtained when discre- tizing SIE with discontinuous coefficients. These algorithms permit essential reducing of computational cost for finding an approximate solution, at that not losing in the quality of other numerical characteristics - they are numerically stable and allow us to check precision in the course of iterations without calculation of approximation of a solution.
B-SPLINE APPROXIMATION OF DISCONTINUOUS FUNCTIONS DEFINED ON A CLOSED CONTOUR IN THE COMPLEX PLANE
(2022) Capcelea, Maria; Capcelea, Titu
In this paper we propose an efficient algorithm for approximating piecewise continuous functions, defined on a closed contour Γ in the complex plane. The function, defined numerically on a finite set of points of Γ, is approximated by a linear combination of B-spline functions and Heaviside step functions, defined on Γ. Theoretical and practical aspects of the convergence of the algorithm are presented, including the vicinity of the discontinuity points.
COLLOCATION AND QUADRATURE METHODS FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS
(Institutul de Matematică şi Informatică al AŞM, 2006) Capcelea, Titu
The computation schemes of collocation and mechanical quadraturemethods for approximate solving of the complete singular integral equations withpiecewise continuous coefficients and a regular kernel with weak singularity are elab-orated. The case when the equations are defined on the unit circumference of thecomplex plane is examined. The sufficient conditions for the convergence of thesemethods in the spaceL2are obtained.
LAURENT-PAD ́E APPROXIMATION FOR LOCATING SINGULARITIES OF MEROMORPHIC FUNCTIONS WITH VALUES GIVEN ON SIMPLE CLOSED CONTOURS
(Institutul de Matematică şi Informatică al AŞM, 2020) Capcelea, Maria; Capcelea, Titu
In the present paper the Pad ́e approximation with Laurent polynomials is examined for a meromorphic function on a finite domain of the c omplex plane. Values of the function are given at the points of a simple closed cont our from this domain. Based on this approximation, an efficient numerical algorith m for locating singular points of the function is proposed.
LOCALIZATION OF SINGULAR POINTS OF MEROMORPHIC FUNCTIONS BASED ON INTERPOLATION BY RATIONAL FUNCTIONS
(2021) Capcelea, Maria; Capcelea, Titu
In this paper we examine two algorithms for localization of singular points of meromorphic functions. Both algorithms apply approximation by interpolation with rational functions. The first one is based on global interpolation and gives the possibility to determine the singular points of the function on a domain that includes a simple closed contour on which the values of the function are known. The second algorithm, based on piecewise interpolation, establishes the poles and the discontinuity points on the contour where the function values are given.
METODA SUBDOMENIILOR LA REZOLVAREA SISTEMELOR DE ECUAŢII INTEGRALE SINGULARE, DEFINITE PE CONTURURI NETEDE ÎNCHISE ÎN PLANUL COMPLEX
(CEP USM, 2008) Capcelea, Maria; Capcelea, Titu
It is proposed a calculation scheme of the sub-domain method for the approximate solving of systems of singular integral equations defined on simple closed and smooth contour in the complex plane. The theoretical justification of this method in the Hölder spaces scale is obtained.
A NUMERICAL METHOD FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS
(CEP USM, 2024) Capcelea, Maria; Capcelea, Titu
The present study is dedicated to developing an efficient computational scheme for solving the Cauchy singular integral equation, defined on a closed and smooth contour in the complex plane. The coefficients and the right-hand side of the equation are piecewise continuous functions, numerically defined on a finite set of points along the contour. The approximate solution is constructed as a linear combination of B-spline functions and Heaviside functions, with coefficients determined using the collocation method. This method generates a sequence of approximations that converge almost uniformly to the exact solution of the equation.