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Ion Pavaloiu (Biography)

$Biography \, of \, Ion \, P\check{a}v\check{a}loiu$

b. 1939 in Romania. Ph.D. in Mathematics in 1971, specialized in Mathematical Analysis, Functional Analysis and Numerical Analysis, with applications to physics and medicine.

Academic positions

1998-present Professor at North University of Baia-Mare

1991-present Senior researcher (I) at “Tiberiu Popoviciu” Institute of Numerical Analysis (ITCP)

1990-present Director of Tiberiu Popoviciu Institute of Numerical Analysis

1990-1991 Senior researcher (II) at Tiberiu Popoviciu Institute of Numerical Analysis

1970-1990 Senior researcher (III) at Tiberiu Popoviciu Institute of Numerical Analysis

1966-1970 Researcher at Tiberiu Popoviciu Institute of Numerical Analysis

1962-1966 Research assistant at Tiberiu Popoviciu Institute of Numerical Analysis

Membership in professional societies

The Romanian Mathematical Society

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 cu 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

Current research in the following areas:

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

Research activities:

Deputy chief Editor of the journal ”Revue D'Analyse NumÃ�rique et de ThÃ�orie de L'Approximation”.

Member in the Editorial board of the journal ”Mathematica”

Research areas:

Selected Publications (from a list of over 100 published papers)

$I. \, P\check{a}v\check{a}loiu$, La r�solution des syst�mes d'�quations opp�rationnelles à l'aide des m�thodes it�ratives, Mathematica, 11, (34), (1969), pp.137-141. (M.R. 41 , No. 4787).

$I. \, P\check{a}v\check{a}loiu$, Int�rpolation dans des �spaces lin�aires norm�es et applications, Mathematica, 12 (35), 1 (1970), pp.149-158. (M.R. 45., No. 9031).

$I. \, P\check{a}v\check{a}loiu$, Sur les procedées itérative á un order Ã�levÃ� de convergence, Mathématica, 12(35) 2 (1970), pp.309-324. (M.R. 40, No. 4245).

$I. \, P\check{a}v\check{a}loiu$, Sur l'approximation des solutions des equations á l'aide des suites á éléments dans un espace de Banach, Mathematica, Revue d'analyse numérique et de la théorie de l'approximation, Tom 5, 1, (1976), pp.63-67. (M.R. 58 , No. 31821).

$I. \, P\check{a}v\check{a}loiu$, Une généralisation de methode de Newton, Mathematica, 20, (43), 1, (1978), pp.45-52. (M.R. 80d: 65073).

$I. \, P\check{a}v\check{a}loiu$, Une variante de méthode de Newton, Revue d'analyse numérique et de la théorie dÃ� l'approximation, 7, 1, (1978), PP.95-99. (M.R. 80g: No. 47078).

$I. \, P\check{a}v\check{a}loiu$, Sur l'order de convergence des m�thodes d'it�ration, Mathematica, 23, (46), 1, (1981), pp.261-272). (M.R. 83m: 40002).

$I. \, P\check{a}v\check{a}loiu$, La résolution des equations par intÃ�rpolation, MathÃ�matica, 23, (46), 1, (1981), pp.61-72. (M.R. 83g: 65064b).

$I. \, P\check{a}v\check{a}loiu$, I. Sherb, Sur des méthodes itératives de type intèrpolatoire á vitèsse de convergence optimale, Revue d'analyse numérique et de la thÃ�orie de l'approximation, 12, 1, (1983), pp.83-88. (M.R. 85h: 65107).

$I. \, P\check{a}v\check{a}loiu$, 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, $I. \, P\check{a}v\check{a}loiu$, I. Sherb, M�thodes it�ratives optimales de type Steffensen obtenues par interpolation inv�rse. Preprint nr.1, (1983). Seminar on functional analysis and numerical methods, pp.81-88.

C. Iancu, $I. \, P\check{a}v\check{a}loiu$, Resolution des equations à l'aide des fonctions splines d'interpolation inv�rse. Preprint nr.1,

C. Iancu, $I. \, P\check{a}v\check{a}loiu$, La resolution des �quations par interpolation inverse de type Hermite, Mathematica (Cluj), 26 (49) (1984), No 2, pp.115-123 (M.R. 86k: 65037).

C. Iancu, $I. \, P\check{a}v\check{a}loiu$, Resolution des equations à l'aide des fonctions rationnelles d'interpolation inv�rse, Preprint nr.1, (1985), pp.71-78. Seminar on functional analysis and numerical methods. (M.R. 832504).

C. Iancu, T. Oproiu, $I. \, P\check{a}v\check{a}loiu$, Inverse interpolation spline with applications to the equation solving, Preprint nr.1 (1986), pp.67-84. Seminar on functional analysis and numerical methods.

$I. \, P\check{a}v\check{a}loiu$, La convergence de certaines mÃ�thodes itératives pour résoudre certaines equations operationnelles, Preprint No.1, (1986), pp.127-132. Seminar on functional analysis and numerical methods.



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Keywords:  functional analysis, numerical analysis, mathematical analysis, analysis

Cross-references: type, computer, mechanics, Banach spaces, nonlinear equations, functions, systems, theorems, algorithm, relation
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