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The Scientific Work of Gradimir V. Milovanović

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 42))

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Abstract

A detailed account of Prof. G.V. Milovanović’s mathematical work, on the occasion of his 60th birthday, is given. He obtained important results in several fields of Numerical Analysis and Approximation Theory. The topics to which he made his most important contributions include: Orthogonal polynomials and systems; Polynomials (extremal problems, inequalities, and zeros); Approximations by polynomials and splines; Quadrature processes.

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References

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  11. G.V. Milovanović, M.S. Petković: On the convergence order of a modified method for simultaneous finding polynomial zeros, Computing 30 (1983), 171–178.

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  21. W. Gautschi, G.V. Milovanović: Spline approximations to spherically symmetric distributions, Numer. Math. 49 (1986), 111–121.

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  25. G.V. Milovanović: Various extremal problems of Markov’s type for algebraic polynomials, Facta Univ. Ser. Math. Inform. 2 (1987), 7–28.

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  29. M. Frontini, W. Gautschi, G.V. Milovanović: Moment-preserving spline approximation on finite intervals, Numer. Math. 50 (1987), 503–518.

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  32. G.V. Milovanović, M.S. Petković: Extremal problems for Lorentz classes of nonnegative polynomials in L 2 metric with Jacobi weight, Proc. Am. Math. Soc. 102 (1988), 283–289.

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  33. G.V. Milovanović, M.A. Kovačević: Moment-preserving spline approximation and Turán quadratures, In: Numerical mathematics (Singapore, 1988), pp. 357–365, ISNM, Vol. 86, Birkhäuser, Basel, 1988.

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  35. G.V. Milovanović, P.M. Rajković: Geronimus concept of orthogonality for polynomials orthogonal on a circular arc, Rend. Mat. Appl. 10 (1990), 383–390.

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  41. L. Gori, M.L. Lo Cascio, G.V. Milovanović: The s-orthogonal polynomials: a method of construction, In: IMACS Annals on Computing and Applied Mathematics, Vol. 9: Orthogonal Polynomials and Their Applications (C. Brezinski, L. Gori, A. Ronveaux, eds.), pp. 281–285, Baltzer, Basel, 1991.

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  44. G.V. Milovanović: Recurrence relation for a class of polynomials associated by the generalized Hermite polynomials, Publ. Inst. Math. (Beograd) (N.S.) 54 (68) (1993), 35–37.

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  45. G.V. Milovanović, D.S. Mitrinović, Th.M. Rassias: On some Turán’s extremal problems for algebraic polynomials, In: Topics in Polynomials of One and Several Variables and Their Applications: A Mathematical Legaci of P.L. Chebyshev (1821–1894) (Th.M. Rassias, H.M. Srivastava, A. Yanushauskas, eds.), pp. 403–433, World Scientific, Singapore, 1993.

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  46. G.V. Milovanović, I.Ž. Milovanović, L.Z. Marinković: Extremal problems for polynomials and their coefficients, In: Topics in Polynomials of One and Several Variables and Their Applications: A Mathematical Legaci of P.L. Chebyshev (1821–1894) (Th.M. Rassias, H.M. Srivastava, A. Yanushauskas, eds.), pp. 435–455, World Scientific, Singapore, 1993.

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  47. G.V. Milovanović, D.S. Mitrinović, Th.M. Rassias: Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific Publ. Co., Singapore, 1994, xiv + 822 pp.

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  48. A. Guessab, G.V. Milovanović: Extremal problems of Markov’s type for some differential operators, Rocky Mt. J. Math. 24 (1994), 1431–1438.

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  50. A. Guessab, G.V. Milovanović: Weighted L 2 -analogues of Bernstein’s inequality and classical orthogonal polynomials, J. Math. Anal. Appl. 82 (1994), 244–249.

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  51. G.V. Milovanović, A. Guessab: An estimate for coefficients of polynomials in L 2 norm, Proc. Am. Math. Soc. 120 (1994), 165–171.

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  52. G.V. Milovanović: Summation of series and Gaussian quadratures, In: Approximation and Computation (R.V.M. Zahar, ed.), pp. 459–475, ISNM Vol. 119, Birkhäuser, Basel, 1994.

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  53. G.V. Milovanović: Summation of slowly convergent series via quadratures, In: Advances in Numerical Methods and Applications (I.T. Dimov, Bl. Sendov, P.S. Vassilevski, eds.), pp. 154–161, World Scientific, Singapore, 1994.

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  54. G.V. Milovanović: Extremal problems for polynomials: old and new results, In: Proceedings Open Problems in Approximation Theory (B. Bojanov, ed.), pp. 138–155, SCT Publishing, Singapore, 1994.

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  55. G.V. Milovanović: Some nonstandard types of orthogonality (A survey), Filomat 9 (1995), 517–542.

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  56. G.V. Milovanović: Expansions of the Kurepa function, Publ. Inst. Math. (Beograd) (N.S.) 57 (71) (1995), 81–90.

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  57. G.V. Milovanović: Summation of series and Gaussian quadratures, II, Numer. Algorithms 10 (1995), 127–136.

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  58. G.V. Milovanović: Generalized Hermite polynomials on the radial rays in the complex plane, In: Theory of Functions and Applications, Collection of Works Dedicated to the Memory of M.M. Djrbashian (H.B. Nersessian, ed.), pp. 125–129, Yerevan, Louys Publishing House, 1995.

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  59. M.A. Kovačević, G.V. Milovanović: Spline approximation and generalized Turán quadratures, Portugal. Math. 53 (1996), 355–366.

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  60. G.V. Milovanović: A sequence of Kurepa’s functions, Scientific Review, Ser. Sci. Eng. 19–20 (1996), 137–146.

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  61. W. Gautschi, G.V. Milovanović: S-orthogonality and construction of Gauss-Turán type quadrature formulae, J. Comput. Appl. Math. 86 (1997), 205–218.

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  62. G.V. Milovanović, I.Ž. Milovanović: Discrete inequalities of Wirtinger’s type for higher differences, J. Inequal. Appl. 1 (1997), 301–310.

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  63. G.V. Milovanović, A.K. Varma: On Birkhoff (0, 3) and (0, 4) quadrature formulae, Numer. Funct. Anal. Optim. 18 (1997), 427–433.

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  64. Lj.M. Kocić, G.V. Milovanović: Shape preserving approximations by polynomials and splines, Comput. Math. Appl. 33 (1997), 59–97.

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  65. G.V. Milovanović, P.S. Stanimirović: On Moore-Penrose inverse of block matrices and full-rank factorization, Publ. Inst. Math. (Beograd) (N.S.) 62 (76) (1997), 26–40.

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  66. G.V. Milovanović: A class of orthogonal polynomials on the radial rays in the complex plane, J. Math. Anal. Appl. 206 (1997), 121–139.

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  67. G.V. Milovanović: Integral inequalities for algebraic polynomials, In: General Inequalities 7 (C. Bandle, ed.), pp. 17–25, ISNM Vol. 123, Birkhäuser, Basel, 1997.

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  68. G.V. Milovanović: Orthogonal polynomial systems and some applications, In: Inner Product Spaces and Applications (Th.M. Rassias, ed.), pp. 115–182, Pitman Res. Notes Math. Ser. 376, Longman, Harlow, 1997.

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  69. B. Danković, G.V. Milovanović, S.Lj. Rančić: Malmquist and Müntz orthogonal systems and applications, In: Inner Product Spaces and Applications (Th.M. Rassias, ed.), pp. 22–41, Pitman Res. Notes Math. Ser. 376, Longman, Harlow, 1997.

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  71. G.V. Milovanović: Orthogonal polynomials on the radial rays and an electrostatic interpretation of zeros, Publ. Inst. Math. (Beograd) (N.S.) 64 (78) (1998), 53–68.

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  72. G.V. Milovanović, B. Danković, S.Lj. Rančić: Some Müntz orthogonal systems, J. Comput. Appl. Math. 99 (1998), 299–310.

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  73. G.V. Milovanović: Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures, Comput. Math. Appl. 36 (1998), 19–39.

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  76. G.V. Milovanović: Extremal problems for restricted polynomial classes in L p norm, In: Approximation Theory: In Memory of A.K. Varma (N.K. Govil, R.N. Mohapatra, Z. Nashed, A. Sharma, J. Szabados, eds.), Monogr. Textbooks Pure Appl. Math., Vol. 212, pp. 405–432, Marcel Dekker, New York, 1998.

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  79. G.V. Milovanović: A note to the paper “On a new class of polynomials” by C.L. Parihar and S.K. Harne, J. Indian Acad. Math. 21 (1999), 277–278.

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  80. G.V. Milovanović, D.Dj. Tošić: An extremal problem for the length of algebraic polynomials, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 10 (1999), 31–36.

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  81. G.V. Milovanović: Extremal problems and inequalities of Markov-Bernstein type for polynomials, In: Analytic and Geometric Inequalities and Applications (Th.M. Rassias, H.M. Srivastava, eds.), Mathematics and Its Applications, Vol. 478, pp. 245–264, Kluwer, Dordrecht, 1999.

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  82. X. Li, I. Gutman, G.V. Milovanović: The β-polynomials of complete graphs are real, Publ. Inst. Math. (Beograd) (N.S.) 67 (81) (2000), 1–6.

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  83. G.V. Milovanović: Dragoslav S. Mitrinović (1908–1995), In: Lives and Work of the Serbian Scientists, Biographies and Bibliographies, Vol. 6 (M. Sarić, ed.), pp. 519–581, Serbian Academy of Sciences and Arts, Belgrade, 2000 (Serbian).

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  84. G.V. Milovanović: Some generalized orthogonal systems and their connections, In: Proceedings of the Symposium “Contemporary Mathematics” (Belgrade, 1998) (N. Bokan, ed.), pp. 181–200, Faculty of Mathematics, University of Belgrade, 2000.

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  85. G.V. Milovanović, Th.M. Rassias: Inequalities for polynomial zeros, In: Survey on Classical Inequalities (Th. M. Rassias, ed.), Mathematics and Its Applications, Vol. 517, pp. 165–202, Kluwer, Dordrecht, 2000.

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  86. G.V. Milovanović, Th.M. Rassias: Distribution of zeros and inequalities for zeros of algebraic polynomials, In: Functional Equations and Inequalities (Th. M. Rassias, ed.), Mathematics and Its Applications, Vol. 518, pp. 171–204, Kluwer, Dordrecht, 2000.

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  87. G.V. Milovanović, A.S. Cvetković: Note on a construction of weights in Gauss-type quadrature rule, Facta Univ. Ser. Math. Inform. 15 (2000), 69–83.

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  88. G.V. Milovanović: Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellán, and L. Reichel, eds.), J. Comput. Appl. Math. 127 (2001), 267–286.

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  89. G.V. Milovanović: Contribution and influence of S.B. Prešić to numerical factorization of polynomials, In: A Tribute to S. B. Prešić (Papers Celebrating his 65th Birthday), pp. 47–56, Mathematics Institut SANU, Belgrade, 2001.

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  90. R.P. Agarwal, G.V. Milovanović: Extremal problems, inequalities, and classical orthogonal polynomials, Appl. Math. Comput. 128 (2002), 151–166.

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  91. G. Mastroianni, G.V. Milovanović: Weighted integration of periodic functions on the real line, Appl. Math. Comput. 128 (2002), 365–378.

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  92. G.V. Milovanović: Orthogonal polynomials on the radial rays in the complex plane and applications, Rend. Circ. Mat. Palermo, Serie II, Suppl. 68 (2002), 65–94.

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  93. G.V. Milovanović, M.M. Spalević: Quadrature formulae connected to σ-orthogonal polynomials, J. Comput. Appl. Math. 140 (2002), 619–637.

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  94. G.V. Milovanović, A. Petojević: Generalized factorial functions, numbers and polynomials, Math. Balkanica (N.S.) 16 (2002), 113–130.

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  95. G.V. Milovanović, A.S. Cvetković: Numerical integration of functions with logarithmic end point singularity, Facta Univ. Ser. Math. Inform. 17 (2002), 57–74.

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  96. G. Mastroianni, G.V. Milovanović: Weighted interpolation of functions with isolated singularities, In: Approximation Theory: A volume dedicated to Blagovest Sendov (B. Bojanov, ed.), pp. 310–341, DARBA, Sofia, 2002.

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  97. G.V. Milovanović, M.M. Spalević: Error bounds for Gauss-Turán quadrature formulae of analytic functions, Math. Comp. 72 (2003), 1855–1872.

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  98. G.V. Milovanović, M. Stanić: Construction of multiple orthogonal polynomials by discretized Stieltjes-Gautschi procedure and corresponding Gaussian quadrature, Facta Univ. Ser. Math. Inform. 18 (2003), 9–29.

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  99. G.V. Milovanović, A.S. Cvetković: An application of little 1∕q-Jacobi polynomials to summation of certain series, Facta Univ. Ser. Math. Inform. 18 (2003), 31–46.

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  100. L.N. Djordjević, D.M. Milošević, G.V. Milovanović, H.M. Srivastava: Some finite summation formulas involving multivariable hypergeometric polynomials, Integral Transform. Spec. Funct. 14 (2003), 349–361.

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  101. G.V. Milovanović, A.S. Cvetković: Complex Jacobi matrices and quadrature rules, Filomat 17 (2003), 117–134.

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  102. G.V. Milovanović, A.S. Cvetković: Numerical construction of the generalized Hermite polynomials, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 14 (2003), 49–63.

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  103. A.S. Cvetković, G.V. Milovanović: The Mathematica Package “OrthogonalPolynomials”, Facta Univ. Ser. Math. Inform. 19 (2004), 17–36.

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  104. G.V. Milovanović, A.S. Cvetković: Uniqueness and computation of Gaussian interval quadrature formula for Jacobi weight function, Numer. Math. 99 (2004), 141–162.

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  105. N.P. Cakić, G.V. Milovanović: On generalized Stirling numbers and polynomials, Math. Balkanica (N.S.) 18 (2004), 241–248.

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  106. G.V. Milovanović, M. Stanić: Multiple orthogonal polynomials on the semicircle and corresponding quadratures of Gaussian type, Math. Balkanica (N.S.) 18(2004), 373–387.

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  107. G.V. Milovanović, A.S. Cvetković: Convergence of Gaussian quadrature rules for approximation of certain series, East J. Approx. 10 (2004), 171–187.

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  108. G.V. Milovanović, M.M. Spalević: Error analysis in some Gauss-Turán-Radau and Gauss-Turán-Lobatto quadratures for analytic functions, J. Comput. Appl. Math. 164/165 (2004), 569–586.

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  109. G.V. Milovanović, M.M. Spalević, A.S. Cvetković: Calculation of Gaussian type quadratures with multiple nodes, Math. Comput. Model. 39 (2004), 325–347.

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  110. G.V. Milovanović, A.S. Cvetković: Standard and non-standard quadratures of Gaussian type, In: Approximation Theory: A volume dedicated to Borislav Bojanov (D. K. Dimitrov, G. Nikolov, R. Uluchev, eds.), pp. 186–200, Marin Drinov Academic Publishing House, Sofia, 2004.

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  111. G.V. Milovanović, A.S. Cvetković: Orthogonal polynomials related to the oscillatory-Chebyshev weight function, Bull. Cl. Sci. Math. Nat. Sci. Math. 30 (2005), 47–60.

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  112. G.V. Milovanović, A.S. Cvetković: Gaussian type quadrature rules for Müntz systems, SIAM J. Sci. Comput. 27 (2005), 893–913.

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  113. G.V. Milovanović, M. Stanić: Multiple orthogonality and quadratures of Gaussian type, Rend. Circ. Mat. Palermo, Serie II, Suppl. 76 (2005), 75–90.

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  1. Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000, Belgrade, Serbia

    Aleksandar Ivić

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  1. Dept. Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Walter Gautschi

  2. Dipto. Matematica, Università Basilicata, Contrada Macchia Romana, Potenza, 85100, Italy

    Giuseppe Mastroianni

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    Themistocles M. Rassias

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Ivić, A. (2010). The Scientific Work of Gradimir V. Milovanović. In: Gautschi, W., Mastroianni, G., Rassias, T. (eds) Approximation and Computation. Springer Optimization and Its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6594-3_1

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