PlanetPhysics/Ion Pavaloiu

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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 Num\'erique et de Th\'eorie de L'Approximation.

Member in the Editorial board of the journal Mathematica

Research areas:

 * mechanics
 * computer science
 * Numerical methods in medicine

Selected Publications (from a list of over 100 published papers)
$$I. \, P\check{a}v\check{a}loiu$$, La r\'esolution des syst\`emes d'\'equations opp\'erationnelles \`a l'aide des m\'ethodes it\'eratives, Mathematica, 11, (34), (1969), pp.137-141. (M.R. 41, No. 4787).

$$I. \, P\check{a}v\check{a}loiu$$, Int\'erpolation dans des \'espaces lin\'eaires norm\'ees 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 proced\'ees it\'erative \'a un order \'elev\'e de convergence, Math\'ematica, 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 \'a l'aide des suites \'a \'el\'ements dans un espace de Banach, Mathematica, Revue d'analyse num\'erique et de la th\'eorie de l'approximation, Tom 5, 1, (1976), pp.63-67. (M.R. 58, No. 31821).

$$I. \, P\check{a}v\check{a}loiu$$, Une g\'en\'eralisation 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 m\'ethode de Newton, Revue d'analyse num\'erique et de la th\'eorie d\'e 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\'ethodes d'it\'eration, Mathematica, 23, (46), 1, (1981), pp.261-272). (M.R. 83m: 40002).

$$I. \, P\check{a}v\check{a}loiu$$, La r\'esolution des equations par int\'erpolation, Math\'ematica, 23, (46), 1, (1981), pp.61-72. (M.R. 83g: 65064b).

$$I. \, P\check{a}v\check{a}loiu$$, I. Sherb, Sur des m\'ethodes it\'eratives de type int\`erpolatoire \'a vit\`esse de convergence optimale, Revue d'analyse num\'erique et de la th\'eorie 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 m\'ethodes it\'eratives 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\'ethodes it\'eratives optimales de type Steffensen obtenues par interpolation inv\`erse. 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 \`a l'aide des fonctions splines d'interpolation inv\`erse. Preprint nr.1,

C. Iancu, $$I. \, P\check{a}v\check{a}loiu$$, La resolution des \'equations 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 \`a l'aide des fonctions rationnelles d'interpolation inv\`erse, 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 m\'ethodes it\'eratives pour r\'esoudre certaines equations operationnelles, Preprint No.1, (1986), pp.127-132. Seminar on functional analysis and numerical methods.