Numerical analysis

Research team

Mircea Dumitru Ivan, Neculae Vornicescu, Gheorghe Toader, Ioan Gavrea, Ioan Rasa, Alexandru Mitrea, Vasile Mihesan, Alexandra Ciupa, Silvia Toader, Daniela Rosca, Octavian Mircia Gurzau, Marius Birou, Daria Dumitras, Mircea Dan Rus, Bogdan Gavrea, Adrian Holhos

 

Research fields

• Approximation of functions
• Wavelets
• Linear positive operators
• Asymptotic expansions
• Runge-Kutta methods

 

Recent research project

“Recent Results in Approximation Theory and Numerical Calculus”, research grant funded by CNCSIS A- 858 2004-2006,

Mircea Ivan, project manager, Neculae Vornicescu, Gheorghe Toader, Ioan Gavrea, Ioan Rasa, Alexandru Mitrea, Vasile Mihesan, Alexandra Ciupa, Silvia Toader, Daniela Rosca, Octavian Mircia Gurzau.

 

The main achievements of the research team are as follows: the complete asymptotic expansion for a sequence of divided differences in terms of Bell polynomials; a new generalization of the Flett mean-value theorem; the complete asymptotic expansion of the Kantorovich variant of the Meyer-Koenig and Zeller operators; a new algorithm of Popoviciu-Casteljau type for averaging positive linear operators; new linear positive operators having the optimal rate of convergence; a new Voronovskaja theorem for a Favard-Szasz type operator; the complete asymptotic expansion of power means in terms of Bell polynomials; new approximation properties of some Szasz-Mirakjan type operators; the complete asymptotic expansion of the differential mean value of divided differences for a large class of functions; new Berman type theorems related to the instability of the extended Lagrange convergence process; a new generalization of the classical theorem of Lozinski-Harsiladze relative to a sequence of polynomial operators; new inequalities of Chebyshev and Buzano type; new properties of the Greek means; locally supported rational pre-wavelets on a sphere and new positive cubature formulas on the sphere.

Publications

M. Birou, “Some bivariate piecewise operators”, Creative Mathematics and Informatics, 17 (3), 2009, 313-318.

 

M. Birou, “Blending surfaces on circular domains generated by Birkhoff interpolation”, Automation Computers and Applied Mathematics, 18 (1), 2009, 97-104.

 

A. Ciupa, “Positive linear operators for the approximation in polynomial weighted spaces”, Bulletin of the Allahabad Mathematical Society (BAMS), 24 (2), 2009, 233-240.

 

C. Petra, B. Gavrea, M. Anitescu, F. Potra, “A computational study of the use  of an optimization-based method for simulating large multibody systems”, Optimization Methods and Software, 24 (6), 2009, 871-894.

 

I. Gavrea, “Estimation for Pn-simple functionals”, Results in Mathematics, 53, 2009, 269-277.

 

I. Gavrea, “An extension of the Lupas theoremfor Hermite-Hadamard functionals”, Mathematical Inequalities & Applications, 12 (3), 2009, 537-548.

 

I. Gavrea, “On some inequalities for convex functions”, Journal of Mathematical Inequalities, 4 (3), 2009, 315-321.

 

I. Gavrea, “About the approximation of the gamma functions”, Automation Computers Applied Mathematics, 18 (1), 2009, 113-120.

 

O. M. Gurzau, “About Heron's Formula for cube roote”, Journal of Sience and Arts,Valahia University of Targoviste, Year 9, No1. (10), 2009, 77-80.

 

A. Holhos, “An inequality for a linear discrete operator involving convex functions”, Journal of Mathematical Inequalities, 3 (3), 2009, 383-393.

 

A. Holhos, “Uniform approximation by positive linear operators on noncompact intervals”, Automation Computers Applied Mathematics, 18 (1), 2009, 121-132.

 

M. Ivan, U. Abel, “Over-iterates of Bernstein's operators: A short and elementary proof”, American Mathematical Monthly, 116 (6), 2009, 535-538.

 

M. Ivan, U. Abel, “An answer to Hermann's conjecture on Bleimann-Butzer-Hahn operators”, Journal of Approximation Theory, 160 (1-2), 2009, 304-310.

 

V. Mihesan, “Gamma approximating operators”, Creative Mathematics and Informatics, 17 (3), 2009, 466-472.

 

V. Mihesan, “Modified Beta approximating operatorsof the first and second kind”, Revue d’Analyse Numerique et de Theorie de l’Approximation, 38 (1), 2009, 65-71.

 

V. Mihesan, “On a general class of Beta approximatingoperators of second type”, Studia Universitatis Babes-Bolyai Mathematica,  54 (4), 2009, 91-103.

 

V. Mihesan, “Weibull approximating operators”, Automation Computers Applied Mathematics, 18 (1), 2009, 157-162.

 

I. Raşa, H. Gonska, P. Piţul, “General King-type operators”, Results in Mathematics, 53 (3-4), 2009, 279-286.

 

I. Raşa, H. Gonska, “Asymptotic behaviour of differentiated Bernstein polynomials”, Matematicki Vesnik, 61 (1), 2009, 53-60.

 

I. Raşa, “Positive linear operators preserving linear functions”, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 7 (1), 2009, 105-110.

 

D. Rosca, “On a norm equivalence in L2(S2)”, Results in Mathematics, 53 (3-4), 2009, 399-405.

 

D. Rosca, “Quadrature formulas with equally distributed points on latitudinal points on the sphere”, Electronic Transactions on Numerical Analysis, 35, 2009, 148-163.

 

C. O. Rus, M.-D. Rus, “Computational aspects in probability problems”, Bulletin of University of Agricultural Sciences and Veterinary Medicine, Cluj Napoca – Horticulture, 66 (2), 2009, 752-757.

 

C. O. Rus, M.-D. Rus, “The compression of Shepard interpolation surfaces”, Bulletin of University of Agricultural Sciences and Veterinary Medicine, Cluj Napoca – Horticulture, 66 (2), 2009, 933.

 

S. Toader, I. Costin, “Metode numerice”, Editura Mediamira, Cluj-Napoca, 2009.

 

M. Birou, “Bivariate Approximation Formulas. Applications”, Casa Cartii de Stiinta, Cluj-Napoca, 2008.

 

M. Birou, “Bivariate operators which interpolate some partial derivatives of a function on the vertices of a square”, International Journal of Pure and Applied Mathematics, 46 (3), 2008, 313-320.

 

M. Birou, “Bivariate operators of binomial type”, Automation Computers and Applied Mathematics, 17 (3), 2008, 381-386.

 

A. Ciupa, “Approximation properties of a modified Jakimovski-Leviatan operator”, Automation Computers and Applied Mathematics, 17 (3), 2008, 401-408.

 

B. Gavrea, C. Petra, “Large quadratic programming problems generated by rigid body simulation”, General Mathematics, 16 (4), 2008, 73-79.

 

B. Gavrea, M. Anitescu, F. Potra, “Convergence of a class of semi-implicit time-stepping schemes for nonsmooth rigid multibody dynamics”, SIAM Journal on Optimization, 19 (2), 2008,  969-1001.

 

B. Gavrea, “On some integral inequalities”, Proceedings of the Conference on Inequalities and Applications, Noszvaj (Hungary), September 2007, International Series of Numerical Mathematics, 2008 Birkhauser Verlag Basel/Switzerland, Vol. 157, 91-95.

 

I. Gavrea, “An inequality for convex functions of third order”, Automation Computers and Applied Mathematics, 17 (3), 2008, 443-448.

 

I. Gavrea, “A characterization of the orthogonal polynomials”, General Mathematics, 16 (4), 2008, 81-86.

 

I. Gavrea, “Operators of Bernstein-Stancu type and the monoticity of some sequences involving convex functions”, Proceedings of the Conference on Inequalities and Applications, Noszvaj (Hungary), September 2007, International Series of Numerical Mathematics, 2008 Birkhauser Verlag Basel/Switzerland, Vol. 157, 181-192.

 

O. M. Gurzau, “Convexity and least square approximation”, Journal of Science and Arts, Valahia University of Targoviste, Year 8, No.1 (8), 2008, 47-49.

 

A. Holhos, “The rate of convergence of positive linear operators in weighted spaces”, Automation Computers and Applied Mathematics, 17 (2), 2008, 239-246.

 

M. Ivan, V. Gupta, “Rate of simultaneous approximation for the Bezier variant of certain operators”, Applied Mathematics and Computation, 199 (1), 2008, 392-395.

 

M. Ivan, X.-M. Zeng, U. Abel, “Approximation by a Kantorovich variant of the Bleimann, Butzer and Hahn operators”, Mathematical Inequalities & Applications, 11 (2), 2008, 317-325.

 

M. Ivan, “On the iterates of some positive linear operators”, Automation Computers Applied Mathematics, 17 (2), 2008, 255-258.

 

M. Ivan, “A note on the Stirling formula”, Automation Computers Applied Mathematics, 17 (3), 2008, 459-462.

 

M. Ivan, “A simple solution to Basel problem”, General Mathematics, 16 (4), 2008, 111-113.

 

V. Mihesan, “On a general class of Beta approximating operators”, General Mathematics, 16 (4), 2008, 115-126.

 

V. Mihesan, “The modified Gamma approximating operators”, Automation Computers and Applied Mathematics, 17 (3), 2008, 497-502.

 

V. Mihesan, “Approximation operators generated by Appell polynomials”, Automation Computers and Applied Mathematics, 17 (3), 2008, 503-508.

 

V. Mihesan, “On a general class of Beta approximating operators of the first kind”, Automation Computers and Applied Mathematics, 17 (2), 2008, 267-282.

 

A. I. Mitrea, “Approximations processes in connection with a problem of Sturm-Liouville type”, Studia Universitatis Babes-Bolyai Mathematica, 53 (3), 2008, 49-57.

 

I. Rasa, “A family of sequences”, Automation Computers and Applied Mathematics, 17 (2), 2008, 305-308.

 

C. O. Rus, M.-D. Rus, “Properties of Shepard’s operator – a summing up”, Automation Computers and Applied Mathematics, 17 (3), 2008, 549-556.

 

M.-D. Rus, C. O. Rus, “Transfinite Shepard interpolation”, Bulletin of University of Agricultural Sciences and Veterinary Medicine, Cluj Napoca – Horticulture, 65 (1), 2008, 672.

U. Abel, M. Ivan, “The differential mean value of divided differences”, Journal of Computational Analysis and Applications, 325(1), 2007, 560–570.

 

U. Abel, M. Ivan, “On Bleimann-Butzer-Hahn operators for exponential functions”, Bulletin of the Australian Mathematical Society, 75(3), 2007, 409–415.

 

U. Abel, M. Ivan, Z. Li, “Local approximation by generalized Baskakov-Durrmeyer operators”, Numerical Functional Analysis and Optimization, 28(3-4), 2007, 245–264.

 

D. Rosca, ”Wavelet bases on the sphere obtained by radial projections”, Journal of Fourier Analysis and Applications, 13(4), 2007, 421-434.

 

P. Cheng, D. Cappelleri, B. Gavrea and V. Kumar, Planning and Control of Meso-Scale Manipulation Tasks with Uncertainties, Proceedings of Robotics: Science and Systems Conference, 2007, http://www.roboticsproceedings.org/rss03/index.html.

 

M. Ivan, “On the Leibniz formula for divided differences”, Revue d'Analyse Numerique et de Theorie de l'Approximation, 35(1), 2006, 59–63.

 

I. Gavrea, O. Mircia, “Some Inequalities Related to Ky Fan Inequality”, Automation Computers Applied Mathematics. Scientific Journal, 15(1), 2006, 143–147.

 

I. Gavrea, “On Chebyshev type inequalities involving functions whose derivatives belong to Lp spaces via isotonic functionals”, Journal of Inequalities in Pure and Applied Mathematics, 7(4), 2006, Article 121.

 

I. Gavrea, “Discrete inequalities of Wirtinger's type in normed spaces”, Automation Computers Applied Mathematics. Scientific Journal, 15(1), 2006, 135-141.

 

I. Gavrea, “A general property of the divided differences”, Automation Computers Applied Mathematics. Scientific Journal, 15(1), 2006, 131-133.

 

I. Rasa, “Classes of convex functions associated with Bernstein operators of second kind”, Mathematical Inequalities & Applications, 9(4), 2006, 599-605.

 

J. Prestin, D. Rosca, “On some cubature formulas on the sphere”, Journal of Approximation Theory, 142(1), 2006, 1-19.

 

D. Rosca, “Wavelets defined on closed surfaces”, Journal of Computational Analysis and Applications, 8(2), 2006, 121-132.

 

D. Rosca, ”Fourier series with linear splines on an interval”, Results in Mathematics, 49(1-2), 2006, 171-184.

 

A. Ciupa, “A Voronovskaya Type Theorem for a Positive Linear Operator”, International Journal of Mathematics and Mathematical Sciences, 2006, ID 42368, 7 pages.

 

J. Sandor, G. Toader, “On some exponential means II”, International Journal of Mathematics and Mathematical Sciences, 2006, ID 51937, 9 pages.

 

S. Toader, G. Toader, “Complementaries of Greek means with respect to Lehmer means”, Automation Computers Applied Mathematics. Scientific Journal, 15(1), 2006, 319-324.

 

M. Birou, C. O. Osan, ”Boolean Shepard interpolation”, Studia Univ. Babes-Bolyai, 52(1), 2006, 27-40.

 

F. A. Potra, M. Anitescu, B. Gavrea, J. Trinkle, “A linearly implicit trapezoidal method for stiff multibody dynamics with contact, joints and friction”, International Journal for Numerical Methods in Engineering, 66(7), 2006, 1079-1124.

 

U. Abel, V. Gupta, M. Ivan, “Asymptotic approximation of functions and their derivatives by generalized Baskakov-Szasz-Durrmeyer operators”, Analysis in Theory and Applications, 25(1), 2005, 15-26.

 

U. Abel, M. Ivan, “Asymptotic expansion of a sequence of divided differences with application to positive linear operators”, Journal of Computational Analysis and Applications, 7(1), 2005, 89-101.

 

U. Abel, V. Gupta, M. Ivan, “Rate of convergence of a Kantorovich variant of the Meyer-Koenig and Zeller operators”, Mathematical Inequalities & Applications, 8(1), 2005, 135-146.

 

D. Rosca, “Locally supported rational spline wavelets on the sphere”, Mathematics of Computation, 74(252), 2005, 1803-1829.

 

N. Vornicescu, ”Existence in the Future by Fixed Point Method”, Fixed Point Theory,. 6(1), 2005, 149-154.

 

S. Toader, ”An approximation operator of Stancu type”, Revue d'Analyse Numerique et de Theorie de l'Approximation, 34, 2005, 115-121.

 

M. Birou, ”Biermann interpolation of Birkhoff type”, Revue d'Analyse Numerique et de Theorie de l'Approximation,34(1), 2005, 37-45.

 

A. Ciupa, “A positive linear operator for approximation of functions of two
variables”, Journal of Concrete and Applicable Mathematics, 3(2), 2005, 187-197.

 

A. I. Mitrea, “On the convergence of a class of approximation procedures”, Pure Mathematics and Applications PU. M .A., 15(2-3), 2005, 225-234.

 

U. Abel, V. Gupta, M. Ivan, “The complete asymptotic expansion for a general Durrmeyer variant of the Meyer-Koenig and Zeller operators”, Mathematical and Computer Modelling, 40, 2004, 867-875.

 

U. Abel, M. Ivan, T. Riedel, “The mean value theorem of Flett and divided differences”, Journal of Mathematical Analysis and Application, 295(1), 2004, 1-9.

 

D. Rosca, ”Optimal Haar wavelets on spherical triangulations”, Pure Mathematics and Applications PU. M. A., 15(4), 2004, 429-438.

 

D. Dumitras, “About Adams formula”, Automation Computers Applied Mathematics. Scientific Journal, 13(1), 2004, 83-85.

 

O. M. Gurzau, ”A Modulus of n-Non-convexity”, Automation Computers Applied Mathematics. Scientific Journal,13(1), 2004, 13-16.

 

V. Mihesan, “A method for sumability of hypergeometric function”, Results in Mathematics, 46(1-2), 2004, 73-78.