1 Biography of Ion Păvăloiu

Born in 1939 in Romania.

Ph.D. in Mathematics in 1971, specialized in Mathematical Analysis, Functional Analysis and Numerical Analysis, with applications to physics and medicine.

1.1 Academic positions

1998–present: Professor at North University of Baia-Mare.

1991–present: Senior Researcher (I) at the “Tiberiu Popoviciu” Institute of Numerical Analysis (ITCP).

1990–present: Director of the Tiberiu Popoviciu Institute of Numerical Analysis.

1990–1991: Senior Researcher (II) at the Tiberiu Popoviciu Institute of Numerical Analysis.

1970–1990: Senior Researcher (III) at the Tiberiu Popoviciu Institute of Numerical Analysis.

1966–1970: Researcher at the Tiberiu Popoviciu Institute of Numerical Analysis.

1962–1966: Research Assistant at the Tiberiu Popoviciu Institute of Numerical Analysis.

1.2 Membership in professional societies

The Romanian Mathematical Society.

1.3 Grants

GAR nr. 95/1998 of the Romanian Academy, Theme: “The qualitative study of the perturbations influence on the stability of inexact Newton method” (collaborator).

GAR nr. 97/1999 of the Romanian Academy, Theme: “The relation between the characterizations of the convergence orders of the practical methods for Newton algorithm.”

GAR nr. 6100GR/13 Oct. 2000 with ANSTI, Theme: Convergence theorems for quasi-Newton and inexact Newton methods (collaborator).

GAR nr. 64/2001 of the Romanian Academy, Theme: High order convergence of the successive approximations (collaborator).

Grant nr. 7037/2001 of M.E.C., Theme: “Newton methods for the singular case; the linear convergence” (consultant).

GAR nr. 45/2002 of the Romanian Academy, Theme: High order convergence of the successive approximations (Co-PI).

GAR nr. 19/2003 of the Romanian Academy, Theme: “The error control in floating arithmetic for the finite differences of the Newton-Krylov methods” (Co-PI).

GAR nr. 16/2004 of the Romanian Academy, Theme: Finite difference Newton-Krylov methods.

1.4 Current research in the following areas

• Inverse interpolation method.
• Methods with optimal convergence order within the class of iteration methods.
• The efficiency of numerical calculus and iteration methods with optimal efficiency index.
• The monotonicity of approximating sequences for solutions of equations.
• Iterative methods (Newton, Newton-Krylov, Newton-type) for numerically solving nonlinear systems of equations in Rⁿ.
• Iterative methods (Newton, Chebyshev, Steffensen, etc.) for numerically solving eigenproblems.
• Methods of function approximation.
• Iterative methods for solving nonlinear equations in Banach spaces.
• The stability of numerical methods for solving equations and error evaluation.

1.5 Research activities

Deputy Chief Editor of the journal Revue d’Analyse Numérique et de Théorie de l’Approximation.

Member of the Editorial Board of the journal Mathematica.

1.5.1 Research areas

• mechanics.
• computer science.
• Numerical methods in medicine.

1.6 Selected publications (from a list of over 100 published papers)

I. Păvăloiu, “La résolution des systèmes d’équations opérationnelles à l’aide des méthodes itératives,” Mathematica, 11 (34) (1969), pp. 137–141. (M.R. 41, No. 4787).

I. Păvăloiu, “Interpolation dans des espaces linéaires normés et applications,” Mathematica, 12 (35), 1 (1970), pp. 149–158. (M.R. 45, No. 9031).

I. Păvăloiu, “Sur les procédés itératifs à un ordre élevé de convergence,” Mathematica, 12 (35), 2 (1970), pp. 309–324. (M.R. 40, No. 4245).

I. Păvăloiu, “Sur l’approximation des solutions des équations à l’aide des suites à éléments dans un espace de Banach,” Mathematica, Revue d’analyse numérique et de la théorie de l’approximation, Tome 5, 1 (1976), pp. 63–67. (M.R. 58, No. 31821).

I. Păvăloiu, “Une généralisation de méthode de Newton,” Mathematica, 20 (43), 1 (1978), pp. 45–52. (M.R. 80d:65073).

I. Păvăloiu, “Une variante de méthode de Newton,” Revue d’analyse numérique et de la théorie de l’approximation, 7, 1 (1978), pp. 95–99. (M.R. 80g, No. 47078).

I. Păvăloiu, “Sur l’ordre de convergence des méthodes d’itération,” Mathematica, 23 (46), 1 (1981), pp. 261–272. (M.R. 83m:40002).

I. Păvăloiu, “La résolution des équations par interpolation,” Mathematica, 23 (46), 1 (1981), pp. 61–72. (M.R. 83g:65064b).

I. Păvăloiu and I. Sherb, “Sur des méthodes itératives de type interpolatoire à vitesse de convergence optimale,” Revue d’analyse numérique et de la théorie de l’approximation, 12, 1 (1983), pp. 83–88. (M.R. 85h:65107).

I. Păvăloiu and I. Sherb, “Sur des méthodes itératives optimales,” Preprint nr. 1 (1983), pp. 175–182, Seminar on Functional Analysis and Numerical Methods. (M.R. 85e:65029).

C. Iancu, I. Păvăloiu, and I. Sherb, “Méthodes itératives optimales de type Steffensen obtenues par interpolation inverse,” Preprint nr. 1 (1983), pp. 81–88, Seminar on Functional Analysis and Numerical Methods.

C. Iancu and I. Păvăloiu, “Résolution des équations à l’aide des fonctions splines d’interpolation inverse,” Preprint nr. 1.

C. Iancu and I. Păvăloiu, “La résolution des équations par interpolation inverse de type Hermite,” Mathematica (Cluj), 26 (49) (1984), No. 2, pp. 115–123. (M.R. 86k:65037).

C. Iancu and I. Păvăloiu, “Résolution des équations à l’aide des fonctions rationnelles d’interpolation inverse,” Preprint nr. 1 (1985), pp. 71–78, Seminar on Functional Analysis and Numerical Methods. (M.R. 832504).

C. Iancu, T. Oproiu, and I. Păvăloiu, “Inverse interpolation spline with applications to equation solving,” Preprint nr. 1 (1986), pp. 67–84, Seminar on Functional Analysis and Numerical Methods.

I. Păvăloiu, “La convergence de certaines méthodes itératives pour résoudre certaines équations opérationnelles,” Preprint No. 1 (1986), pp. 127–132, Seminar on Functional Analysis and Numerical Methods.