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The Scientific Work of Gradimir V. Milovanović

  • Aleksandar Ivić
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)

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.

Keywords

Orthogonal Polynomial Extremal Problem Quadrature Formula Quadrature Rule Gaussian Quadrature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D.D. Tošić, G.V. Milovanović: An application of Newton’s method to simultaneous determination of zeros of a polynomial, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 412–No 460 (1973), 175–177.Google Scholar
  2. 2.
    G.V. Milovanović: A method to accelerate iterative processes in Banach space, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 461–No 479 (1974), 67–71.Google Scholar
  3. 3.
    R.Ž. DORDEVIĆ, G.V. Milovanović: A generalization of E. Landau’s theorem, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 498–No 541 (1975), 97–106.Google Scholar
  4. 4.
    G.V. Milovanović: On some integral inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 498–No 541 (1975), 119–124.Google Scholar
  5. 5.
    P.M. Vasić, G.V. Milovanović: On an inequality of Iyengar, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 544–No 576 (1976), 18–24.Google Scholar
  6. 6.
    G.V. Milovanović, J.E. Pečarić: On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 544–No 576 (1976), 155–158.Google Scholar
  7. 7.
    G.V. Milovanović, J.E. Pečarić: Some considerations of Iyengar’s inequality and some related applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 544–No 576 (1976), 166–170.Google Scholar
  8. 8.
    G.V. Milovanović: On some functional inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 599 (1977), 1–59 (Serbian, English summary).Google Scholar
  9. 9.
    G.V. Milovanović, I.Ž. Milovanović: On discrete inequalities of Wirtinger’s type, J. Math. Anal. Appl. 88 (1982), 378–387.Google Scholar
  10. 10.
    G.V. Milovanović, R.Ž. DORDEVIĆ: A generalization of modified Birkhoffoung quadrature formula, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No 735–No 762 (1982), 130–134.Google Scholar
  11. 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.Google Scholar
  12. 12.
    M.S. Petković, G.V. Milovanović: A note on some improvements of the simultaneous method for determination of polynomial zeros, J. Comput. Appl. Math. 9 (1983), 65–69.Google Scholar
  13. 13.
    G.V. Milovanović, I.Ž. Milovanović: Some discrete inequalities of Opial’s type, Acta Sci. Math. (Szeged) 47 (1984), 413–417.Google Scholar
  14. 14.
    W. Gautschi, G.V. Milovanović: On a class of complex polynomials having all zeros in a half disc, In: Numerical methods and approximation theory (Niš, 1984), pp. 49–53, Univ. Niš, Niš, 1984.Google Scholar
  15. 15.
    W. Gautschi, G.V. Milovanović: Polynomials orthogonal on the semicircle, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (July 1985), 179–185.Google Scholar
  16. 16.
    G.V. Milovanović: An extremal problem for polynomials with nonnegative coefficients, Proc. Amer. Math. Soc. 94 (1985), 423–426.Google Scholar
  17. 17.
    W. Gautschi, G.V. Milovanović: Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series, Math. Comp. 44 (1985), 177–190; Supplement to Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series, Math. Comp. 44 (1985), S1–S11.Google Scholar
  18. 18.
    G.V. Milovanović, M.S. Petković: On computational efficiency of the iterative methods for simultaneous approximation of polynomial zeros, ACM Trans. Math. Software 12 (1986), 295–306.Google Scholar
  19. 19.
    G.V. Milovanović, B.P. Acharya, T.N. Pattnaik: On numerical evaluation of double integrals of an analytic function of two complex variables, BIT 26 (1986), 521–526.Google Scholar
  20. 20.
    M.S. Petković, G.V. Milovanović, L.V. Stefanović: Some higher-order methods for the simultaneous approximation of multiple polynomial zeros, Comput. Math. Appl. 12A (1986), 951–962.Google Scholar
  21. 21.
    W. Gautschi, G.V. Milovanović: Spline approximations to spherically symmetric distributions, Numer. Math. 49 (1986), 111–121.Google Scholar
  22. 22.
    W. Gautschi, G.V. Milovanović: Polynomials orthogonal on the semicircle, J. Approx. Theory 46 (1986), 230–250.Google Scholar
  23. 23.
    G.V. Milovanović, I.Ž. Milovanović: A generalization of a result of A. Meir for non-decreasing sequences, Rocky Mountain J. Math. 16 (1986), 237–239.Google Scholar
  24. 24.
    G.V. Milovanović, S. Wrigge: Least squares approximation with constraints, Math. Comp. 46 (1986), 551–565.Google Scholar
  25. 25.
    G.V. Milovanović: Various extremal problems of Markov’s type for algebraic polynomials, Facta Univ. Ser. Math. Inform. 2 (1987), 7–28.Google Scholar
  26. 26.
    W. Gautschi, M.A Kovačević, G.V. Milovanović: The numerical evaluation of singular integrals with coth-kernel, BIT 27 (1987), 389–402.Google Scholar
  27. 27.
    G.V. Milovanović, G. Djordjević: On some properties of Humbert’s polynomials, Fibonacci Quart. 25 (1987), 356–360.Google Scholar
  28. 28.
    W. Gautschi, H. Landau, G.V. Milovanović: Polynomials orthogonal on the semicircle II, Constr. Approx. 3 (1987), 389–404.Google Scholar
  29. 29.
    M. Frontini, W. Gautschi, G.V. Milovanović: Moment-preserving spline approximation on finite intervals, Numer. Math. 50 (1987), 503–518.Google Scholar
  30. 30.
    G.V. Milovanović: Some applications of the polynomials orthogonal on the semicircle, In: Numerical Methods (Miskolc, 1986), pp. 625–634, Colloquia Mathematica Societatis Janos Bolyai, Vol. 50, North-Holland, Amsterdam-New York, 1987.Google Scholar
  31. 31.
    G.V. Milovanović: Construction of s-orthogonal polynomials and Turán quadrature formulae, In: Numerical methods and approximation theory III (Niš, 1987), pp. 311–328, Univ. Niš, Niš, 1988.Google Scholar
  32. 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.Google Scholar
  33. 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.Google Scholar
  34. 34.
    G.V. Milovanović: Complex orthogonality on the semicircle with respect to Gegenbauer weight: Theory and applications, In: Topics in Mathematical Analysis (Th.M. Rassias, ed.), pp. 695–722, Ser. Pure Math., 11, World Sci. Publishing, Teaneck, NJ, 1989.Google Scholar
  35. 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.Google Scholar
  36. 36.
    R.P. Agarwal, G.V. Milovanović: On an inequality of Bogar and Gustafson, J. Math. Anal. Appl. 146 (1990), 207–216.Google Scholar
  37. 37.
    G.V. Milovanović, D.S. Mitrinović, Th.M. Rassias: On some extremal problems for algebraic polynomials in L r norm, In: Generalized Functions and Convergence (Katowice, 1988), pp. 343–354, World Scientific, Singapore, 1990.Google Scholar
  38. 38.
    F. Calió, M. Frontini, G.V. Milovanović: Numerical differentiation of analytic functions using quadratures on the semicircle, Comput. Math. Appl. 22 (1991), 99–106.Google Scholar
  39. 39.
    G.V. Milovanović, Lj.M. Kocić: Integral spline operators in CAGD, Atti Sem. Mat. Fis. Univ. Modena 39 (1991), 433–454.Google Scholar
  40. 40.
    R.P. Agarwal, G.V. Milovanović: A characterization of the classical orthogonal polynomials, Progress in Approximation Theory (P. Nevai, A. Pinkus, eds.), pp. 1–4, Academic, New York, 1991.Google Scholar
  41. 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.Google Scholar
  42. 42.
    G.V. Milovanović, Th.M. Rassias: Inequalities connected with trigonometric sums, In: Constantin Carathéodory: An International Tribute, Vol. II (Th.M. Rassias, ed.), pp. 875–941, World Sci. Publishing, Teaneck, NJ, 1991.Google Scholar
  43. 43.
    G.V. Milovanović: On polynomials orthogonal on the semicircle and applications, J. Comput. Appl. Math. 49 (1993), 193–199.Google Scholar
  44. 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.Google Scholar
  45. 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.Google Scholar
  46. 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.Google Scholar
  47. 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.Google Scholar
  48. 48.
    A. Guessab, G.V. Milovanović: Extremal problems of Markov’s type for some differential operators, Rocky Mt. J. Math. 24 (1994), 1431–1438.Google Scholar
  49. 49.
    G.V. Milovanović, P.M. Rajković: On polynomials orthogonal on a circular arc, J. Comput. Appl. Math. 51 (1994), 1–13.Google Scholar
  50. 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.Google Scholar
  51. 51.
    G.V. Milovanović, A. Guessab: An estimate for coefficients of polynomials in L 2 norm, Proc. Am. Math. Soc. 120 (1994), 165–171.Google Scholar
  52. 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.Google Scholar
  53. 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.Google Scholar
  54. 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.Google Scholar
  55. 55.
    G.V. Milovanović: Some nonstandard types of orthogonality (A survey), Filomat 9 (1995), 517–542.Google Scholar
  56. 56.
    G.V. Milovanović: Expansions of the Kurepa function, Publ. Inst. Math. (Beograd) (N.S.) 57 (71) (1995), 81–90.Google Scholar
  57. 57.
    G.V. Milovanović: Summation of series and Gaussian quadratures, II, Numer. Algorithms 10 (1995), 127–136.Google Scholar
  58. 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.Google Scholar
  59. 59.
    M.A. Kovačević, G.V. Milovanović: Spline approximation and generalized Turán quadratures, Portugal. Math. 53 (1996), 355–366.Google Scholar
  60. 60.
    G.V. Milovanović: A sequence of Kurepa’s functions, Scientific Review, Ser. Sci. Eng. 19–20 (1996), 137–146.Google Scholar
  61. 61.
    W. Gautschi, G.V. Milovanović: S-orthogonality and construction of Gauss-Turán type quadrature formulae, J. Comput. Appl. Math. 86 (1997), 205–218.Google Scholar
  62. 62.
    G.V. Milovanović, I.Ž. Milovanović: Discrete inequalities of Wirtinger’s type for higher differences, J. Inequal. Appl. 1 (1997), 301–310.Google Scholar
  63. 63.
    G.V. Milovanović, A.K. Varma: On Birkhoff (0, 3) and (0, 4) quadrature formulae, Numer. Funct. Anal. Optim. 18 (1997), 427–433.Google Scholar
  64. 64.
    Lj.M. Kocić, G.V. Milovanović: Shape preserving approximations by polynomials and splines, Comput. Math. Appl. 33 (1997), 59–97.Google Scholar
  65. 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.Google Scholar
  66. 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.Google Scholar
  67. 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.Google Scholar
  68. 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.Google Scholar
  69. 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.Google Scholar
  70. 70.
    G.V. Milovanović: S-orthogonality and generalized Turán quadratures: Construction and applications, In: Approximation and Optimization, Vol. I (Cluj-Napoca, 1996) (D.D. Stancu, Gh. Coman, W.W. Breckner, P. Blaga, eds.), pp. 91–106, Transilvania, Cluj-Napoca, Romania, 1997.Google Scholar
  71. 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.Google Scholar
  72. 72.
    G.V. Milovanović, B. Danković, S.Lj. Rančić: Some Müntz orthogonal systems, J. Comput. Appl. Math. 99 (1998), 299–310.Google Scholar
  73. 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.Google Scholar
  74. 74.
    G.V. Milovanović: Life and inequalities: D. S. Mitrinović (1908–1996), In: Recent Progress in Inequalities (G.V. Milovanović, ed.), Mathematics and Its Applications, Vol. 430, pp. 1–10, Kluwer, Dordrecht, 1998.Google Scholar
  75. 75.
    G.V. Milovanović, I.Ž. Milovanović: Discrete inequalities of Wirtinger’s type, In: Recent Progress in Inequalities (G.V. Milovanovic, ed.), Mathematics and Its Applications, Vol. 430, pp. 289–308, Kluwer, Dordrecht, 1998.Google Scholar
  76. 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.Google Scholar
  77. 77.
    G.V. Milovanović, Th.M. Rassias: New developments on Turán’s extremal problems for polynomials, 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. 433–447, Marcel Dekker, New York, 1998.Google Scholar
  78. 78.
    G.V. Milovanović: Müntz orthogonal polynomials and their numerical evaluation, In: Applications and Computation of Orthogonal Polynomials (W. Gautschi, G.H. Golub, and G. Opfer, eds.), pp. 179–202, ISNM, Vol. 131, Birkhäuser, Basel, 1999.Google Scholar
  79. 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.Google Scholar
  80. 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.Google Scholar
  81. 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.Google Scholar
  82. 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.Google Scholar
  83. 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).Google Scholar
  84. 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.Google Scholar
  85. 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.Google Scholar
  86. 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.Google Scholar
  87. 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.Google Scholar
  88. 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.Google Scholar
  89. 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.Google Scholar
  90. 90.
    R.P. Agarwal, G.V. Milovanović: Extremal problems, inequalities, and classical orthogonal polynomials, Appl. Math. Comput. 128 (2002), 151–166.Google Scholar
  91. 91.
    G. Mastroianni, G.V. Milovanović: Weighted integration of periodic functions on the real line, Appl. Math. Comput. 128 (2002), 365–378.Google Scholar
  92. 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.Google Scholar
  93. 93.
    G.V. Milovanović, M.M. Spalević: Quadrature formulae connected to σ-orthogonal polynomials, J. Comput. Appl. Math. 140 (2002), 619–637.Google Scholar
  94. 94.
    G.V. Milovanović, A. Petojević: Generalized factorial functions, numbers and polynomials, Math. Balkanica (N.S.) 16 (2002), 113–130.Google Scholar
  95. 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.Google Scholar
  96. 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.Google Scholar
  97. 97.
    G.V. Milovanović, M.M. Spalević: Error bounds for Gauss-Turán quadrature formulae of analytic functions, Math. Comp. 72 (2003), 1855–1872.Google Scholar
  98. 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.Google Scholar
  99. 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.Google Scholar
  100. 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.Google Scholar
  101. 101.
    G.V. Milovanović, A.S. Cvetković: Complex Jacobi matrices and quadrature rules, Filomat 17 (2003), 117–134.Google Scholar
  102. 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.Google Scholar
  103. 103.
    A.S. Cvetković, G.V. Milovanović: The Mathematica Package “OrthogonalPolynomials”, Facta Univ. Ser. Math. Inform. 19 (2004), 17–36.Google Scholar
  104. 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.Google Scholar
  105. 105.
    N.P. Cakić, G.V. Milovanović: On generalized Stirling numbers and polynomials, Math. Balkanica (N.S.) 18 (2004), 241–248.Google Scholar
  106. 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.Google Scholar
  107. 107.
    G.V. Milovanović, A.S. Cvetković: Convergence of Gaussian quadrature rules for approximation of certain series, East J. Approx. 10 (2004), 171–187.Google Scholar
  108. 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.Google Scholar
  109. 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.Google Scholar
  110. 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.Google Scholar
  111. 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.Google Scholar
  112. 112.
    G.V. Milovanović, A.S. Cvetković: Gaussian type quadrature rules for Müntz systems, SIAM J. Sci. Comput. 27 (2005), 893–913.Google Scholar
  113. 113.
    G.V. Milovanović, M. Stanić: Multiple orthogonality and quadratures of Gaussian type, Rend. Circ. Mat. Palermo, Serie II, Suppl. 76 (2005), 75–90.Google Scholar
  114. 114.
    G.V. Milovanović, A.S. Cvetković: Some inequalities for symmetric functions and an application to orthogonal polynomials, J. Math. Anal. Appl. 311 (2005), 191–208.Google Scholar
  115. 115.
    G.V. Milovanović, M.M. Spalević: An error expansion for some Gauss-Turán quadratures and L 1 -estimates of the remainder term, BIT 45 (2005), 117–136.Google Scholar
  116. 116.
    G.V. Milovanović, A.S. Cvetković: Remarks on “Orthogonality of some sequences of the rational functions and Müntz polynomials”, J. Comput. Appl. Math. 173 (2005), 383–388.Google Scholar
  117. 117.
    G.V. Milovanović, M.M. Spalević: Bounds of the error of Gauss–Turán-type quadratures, J. Comput. Appl. Math. 178 (2005), 333–346.Google Scholar
  118. 118.
    G.V. Milovanović, A.S. Cvetković: Orthogonal polynomials and Gaussian quadrature rules related to oscillatory weight functions, J. Comput. Appl. Math. 179 (2005), 263–287.Google Scholar
  119. 119.
    G.V. Milovanović, A.S. Cvetković: Gauss-Laguerre interval quadrature rule, J. Comput. Appl. Math. 182 (2005), 433–446.Google Scholar
  120. 120.
    G.V. Milovanović, A.S. Cvetković, M.M. Matejić: On positive definiteness of some linear functionals, Stud. Univ. Babeş-Bolyai Math. 51 (2006), no. 4, 157–166.Google Scholar
  121. 121.
    G.V. Milovanović, M.M. Spalević: Gauss-Turán quadratures of Kronrod type for generalized Chebyshev weight functions, Calcolo 43 (2006), 171–195.Google Scholar
  122. 122.
    G.V. Milovanović, M.M. Spalević: Quadrature rules with multiple nodes for evaluating integrals with strong singularities, J. Comput. Appl. Math. 189 (2006), 689–702.Google Scholar
  123. 123.
    G.V. Milovanović, A.S. Cvetković: Gauss-Radau and Gauss-Lobatto interval quadrature rules for Jacobi weight function, Numer. Math. 102 (2006), 523–542.Google Scholar
  124. 124.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Two conjectures for integrals with oscillatory integrands, Facta Univ. Ser. Math. Inform. 22 (2007), 77–90.Google Scholar
  125. 125.
    G. Mastroianni, G.V. Milovanović: Polynomial approximation on unbounded intervals by Fourier sums, Facta Univ. Ser. Math. Inform. 22 (2007), 155–164.Google Scholar
  126. 126.
    D. Dolićanin, G.V. Milovanović, V.G. Romanovski: Linearizablity conditions for a cubic system, Appl. Math. Comput. 190 (2007), 937–945.Google Scholar
  127. 127.
    G.V. Milovanović, A.S. Cvetković: Gauss-Hermite interval quadrature rule, Comput. Math. Appl. 54 (2007), 544–555.Google Scholar
  128. 128.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Gaussian quadratures for oscillatory integrands, Appl. Math. Lett. 20 (2007), 853–860.Google Scholar
  129. 129.
    G.V. Milovanović, M.M. Spalević: Monotonicity of the error term in Gauss-Turán quadratures for analytic functions, ANZIAM J. 48 (2007), 567–581.Google Scholar
  130. 130.
    G.V. Milovanović, A.S. Cvetković: A note on three-step iterative methods for nonlinear equations, Stud. Univ. Babeş-Bolyai Math. 52 (2007), no. 3, 137–146.Google Scholar
  131. 131.
    G.V. Milovanović, A.S. Cvetković, Z.M. Marjanović: Connection of semi-integer trigonometric orthogonal polynomials with Szegő polynomials, 394–401, Lecture Notes in Comput. Sci., 4310, Springer, Berlin, 2007.Google Scholar
  132. 132.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Trigonometric orthogonal systems and quadrature formulae with maximal trigonometric degree of exactness, 402–409, Lecture Notes in Comput. Sci., 4310, Springer, Berlin, 2007.Google Scholar
  133. 133.
    G.V. Milovanović, A.S. Cvetković: Logarithmic modification of the Jacobi weight function, Stud. Univ. Babeş-Bolyai Math. 52 (2007), no. 4, 143–153.Google Scholar
  134. 134.
    G.V. Milovanović, M.M. Spalević: A note on the bounds of the error of Gauss-Turán-type quadratures, J. Comput. Appl. Math. 200 (2007), 276–282.Google Scholar
  135. 135.
    G. Mastroianni, G.V. Milovanović: Interpolation Processes – Basic Theory and Applications, Springer Monographs in Mathematics, Springer, Berlin, 2008, xiv + 444 pp.Google Scholar
  136. 136.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Trigonometric orthogonal systems and quadrature formulae, Comput. Math. Appl. 56 (2008), 2915–2931.Google Scholar
  137. 137.
    G.V. Milovanović: Quadrature processes – development and new directions, Bull. Cl. Sci. Math. Nat. Sci. Math. 33 (2008), 11–41.Google Scholar
  138. 138.
    A.S. Cvetković, G.V. Milovanović: Positive definite solutions of some matrix equations, Linear Algebra Appl. 429 (2008), 2401–2414.Google Scholar
  139. 139.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Explicit formulas for five-term recurrence coefficients of orthogonal trigonometric polynomials of semi-integer degree, Appl. Math. Comput. 198 (2008), 559–573.Google Scholar
  140. 140.
    G.V. Milovanović, M.M. Spalević, M.S. Pranić: Maximum of the modulus of kernels in Gauss-Turán quadratures, Math. Comp. 77 (2008), 985–994.Google Scholar
  141. 141.
    G.V. Milovanović, M.M. Spalević, M.S. Pranić: On the remainder term of Gauss-Radau quadratures for analytic functions, J. Comput. Appl. Math. 218 (2008), 281–289.Google Scholar
  142. 142.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Orthogonal polynomials for modified Gegenbauer weight and corresponding quadratures, Appl. Math. Letters 22 (2009), 1189–1194.Google Scholar
  143. 143.
    G.V. Milovanović, A.S. Cvetković, M.P. Stanić: Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness, Numer. Math. 112 (2009), 425–448.Google Scholar
  144. 144.
    G.V. Milovanović, A.S. Cvetković: Numerical integration with complex Jacobi weight function, 20–31, Lecture Notes in Comput. Sci., 5434, Springer, Berlin, 2009.Google Scholar
  145. 145.
    G.V. Milovanović, M.M. Spalević, M.S. Pranić: Error estimates for Gauss-Turán quadratures and their Kronrod extensions, IMA J. Numer. Anal. 29 (2009), 486–507.Google Scholar
  146. 146.
    G.V. Milovanović, M.M. Spalević, M.S. Pranić: Error estimates for Gaussian quadratures of analytic functions, J. Comput. Appl. Math. 233 (2009), 802–807.Google Scholar
  147. 147.
    G. Mastroianni, G.V. Milovanović: Some numerical methods for second kind Fredholm integral equation on the real semiaxis, IMA J. Numer. Anal. 29 (2009), 1046–1066.Google Scholar
  148. 148.
    G.V. Milovanović, A.S. Cvetković: Nonstandard Gaussian quadrature formulae based on operatror values, Adv. Comput. Math. 32 (2010), 431–486.Google Scholar
  149. 149.
    G. Mastroianni, G.V. Milovanović: Well-conditioned matrices for numerical treatment of Fredholm integral equations of the second kind, Numer. Linear Algebra Appl. 16 (2009), 995–1011.Google Scholar
  150. 150.
    G.V. Milovanović, M.M. Spalević, M.S. Pranić: Bounds of the error of Gauss-Tur-type quadratures, II, Appl. Numer. Math. 60 (2010), 1–9.Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Serbian Academy of Sciences and ArtsBelgradeSerbia

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