Geno Petkov Nikolov

Geno Petkov Nikolov

Professor
DSc

Numerical Methods and Algorithms

Email: 
geno@fmi.uni-sofia.bg
Phone: 
+359 2 8161-592 (8161-587)
Room: 
FMI-520
Office hours: 

Tuesday 15:00 - 16:00; Wednesday 15:00 - 16:00

Publications

  1. G. Nikolov, A comparison theorem in the theory of quadrature formulas, Math. Balkanica 2, 1(1988), 3-10.
  2. G. Nikolov and R. Uluchev, A comparison theorem for Tchebysheff polynomials, Serdica 14 (1988), 95-97.
  3. G. Nikolov, Existence and uniqueness of Hermite-Birkhoff Gaussian quadrature formulae, Calcolo 26 (1989), 41-59.
  4. B. Bojanov and G. Nikolov, Comparison of Birkhoff type quadrature formulae, Math. Comp. 54 (1990), 627-648.
  5. G. Nikolov, On the monotonicity of sequences of quadrature formulae, Numer. Math. 62 (1992), 557-565
  6. G. Nikolov, Gaussian quadrature formulae for splines. В : "Numerische Integration, IV" (G. Hämmerlin and H. Brass Eds.), ISNM 112, 267-281, Birkhäuser, Basel, 1993.
  7. G. Nikolov, Exit criteria and monotonicity of the remainders of Euler-MacLaurin quadrature formulae. В: "Open Problems in Approximation Theory" (B. Bojanov Ed.), 156-162, SCT Publishing, Singapore, 1994.
  8. P. Köhler and G. Nikolov, Error bounds for Gauss type quadrature formulae related to spaces of splines with equidistant knots, J. Approx. Theory 81 (1995), 368-388.
  9. P. Köhler and G. Nikolov, Error bounds for optimal definite quadrature formulae, J. Approx. Theory 81 (1995), 397-405.
  10. G. Nikolov, Asymptotically optimal definite quadrature formulae, ZAMM 75 (1995) SII, 653-654.
  11. G. Nikolov, On certain definite quadrature formulae, J. Comp.  Appl.  Math. 75 (1996), 329-343.
  12. B. Bojanov and G. Nikolov, Duffin and Schaeffer type inequality for ultraspherical polynomials, J. Approx. Theory 84 (1996), 129-138.
  13. L. Milev and G. Nikolov, On the inequality of I. Schur, J. Math Anal. Appl.  216 (1997), 421-437.
  14. G. Nikolov, On the remainder of the Gauss-Lobatto quadrature formula associated with the second Chebyshev weight function  B: Proceedings of the Sixth International Colloquium on Numerical Analysis and Computer Science with Applications, August 13-17, 1997, Plovdiv, Bulgaria (E. Minchev Ed.), Academic Publications, 137-144.
  15. G. Nikolov, On certain Duffin and Schaeffer type inequalities, J.  Approx. Theory 93 (1998), 157-176.
  16. K.-J. Förster, P. Köhler and G. Nikolov, Monotonicity and stopping rules for compound Gauss-type quadrature formulae, East J. Approx.  4 (1998), 55-74.
  17. G. Nikolov, An inequality of Duffin-Schaeffer-Schur type, Annuaire Univ. Sofia 90 (1998), 109-123.
  18. D.B. Hunter and G. Nikolov, Gaussian quadrature of Chebyshev polynomials, J. Comp. Appl. Math. 94 (1998), 123-131.
  19. G. Nikolov, An inequality for polynomials with elliptic majorant,  J. Inequal. Appl. 4 (1999), 315-325.
  20. B. Bojanov, D. Dryanov, W. Haussmann and G. Nikolov, Best one-sided L1-approximation by blending functions. В: Advances in Multivariate Approximation (W. Haussmann, K. Jetter and M. Reimer Eds.), Math. Research v. 107, ISBN 3-527-40236-5, Wiley - VCH, Berlin 1999, 85-106.
  21. D.B. Hunter and G. Nikolov, Gegenbauer weight functions admitting L2 Duffin and Schaeffer type inequalities, B: Applications and computation of orthogonal polynomials (W. Gautschi, G. Golub and G. Opfer, eds.), Birkhäuser, Basel, 1999, ISNM 131, 121-131.
  22. D.B. Hunter and G. Nikolov, On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions, Math. Comp. 69 (2000), 269-282.
  23. B. Bojanov, W. Haussmann and G. Nikolov, Bivariate polynomials of least deviation, Canad. J. Math.  53 (3) (2001), 489-505.
  24. G. Nikolov, Inequalities of Duffin-Schaeffer type, SIAM J. Math. Anal. 33 (3) (2001), 686-698.
  25. G. Nikolov, On the weights of nearly Gaussian quadrature formulae, East J. Approx.  7 (2001), 115-120.
  26. V. Gushev and G. Nikolov, On some cubature formulae using mixed type data. В: Recent Progress in Multivariate Approximation (W. Haussmann, K. Jetter and M. Reimer, Eds.), ISNM 137, Birkhäuser, Basel, 2001, 163-184.
  27. G. Nikolov, Snake polynomials and Markov-type inequalities, B: Approximation Theory: a volume dedicated to Blagovest Sendov (B. Bojanov, Ed.), Darba, Sofia, 2002, 342-352.
  28. G. Nikolov, The Christoffel function for the Hermite weight is bell-shaped, J. Approx. Theory 125 (2) (2003), 145-150.
  29. G. Nikolov, Markov-type inequalities in the L2-norms induced by the Tchebysheff weights, Arch. Ineq. Appl. 1 (2003), 361-376.
  30. G. Nikolov, An extremal property of Hermite polynomials, J. Math. Anal. Appl.  290 (2004), 405-413.
  31. G. Nikolov and R. Uluchev, Inequalities for real-root polynomials. Proof of a conjecture of Foster and Krasikov, в: Approximation Theory: A volume dedicated to Borislav Bojanov (D.K. Dimitrov, G. Nikolov, and R. Uluchev, Eds.) , Prof.  Marin Drinov Academic Publ. House, Sofia 2004, 201-216.
  32. G. Nikolov, An extension of an inequality of Duffin and Schaeffer, Constr. Approx.  21 (2005), 181-191.
  33. G. Nikolov, Inequalities of Duffin-Schaeffer type, II,  East J. Approx. 11 (2) (2005), 147-168.
  34. G. Nikolov, An extension of an inequality of I. Schur, Math. Nachr. 278 (10) (2005).
  35. G. Nikolov, Polynomial inequalities of Markov and Duffin-Schaeffer type. В: Constructive theory of functions. Varna 2005 (B. Bojanov, ed.), Prof.  Marin Drinov Academic Publ. House, Sofia, 2006, 201-246.
  36. V. Gushev and G. Nikolov, Formulae for calculation of normal probability, NMA 2006 (T. Boyanov et al., Eds.), Lecture Notes in Computer Sciences, Springer-Verlag 2140 (2007), 369-377.
  37. G. Nikolov, Cubature formulae for the disk using Radon projections, East J. Approx. 14, 4(2008), 401-410.
  38.  V. Gushev and G. Nikolov, Modified product cubature formulae, J. Comp. Appl. Math.  224 (2009), 465-475. 
  39. G. Nikolov and C. Simian, Gauss-type quadrature formulae for parabolic splines with equidistant knots. В:  Approximation  and Computation - In Honor of Gradimir V. Milovanovic, pp. 207 - 229 (W. Gautschi, G. Mastroianni, Th. M. Rassias, eds.), Springer Optimization and its Applications, Springer Verlag, Berlin - Heidelberg - New York, 2010.
  40. D. K. Dimitrov and G. Nikolov, Sharp bounds for the extreme zeros of classical orthogonal polynomials, J. Approx. Theory 162 (10) (2010), 1793-1804 
  41. G. P. Nikolov and P. B. Nikolov, Quadrature formulae based on interpolation by parabolic splines, East J. Approx. 16, 3(2010), 219-233.
  42. G. Nikolov and A. Alexandrov, An inequality of Duffin-Schaeffer type for Hermite polynomials, в: Constructive Theory of Functions, Sozopol 2010 (G. Nikolov and R. Uluchev, Eds.),  Prof.  Marin Drinov Academic Publ. House, Sofia, 2012, 9-20.
  43. G. Nikolov and A. Shadrin, On Markov-Duffin-Schaeffer inequalities with a majorant, в: Constructive Theory of Functions, Sozopol 2010 (G. Nikolov and R. Uluchev, Eds.),  Prof.  Marin Drinov Academic Publ. House, Sofia, 2012, 227-264.
  44. G. Nikolov and A. Alexandrov, On the behavior of Gegenbauer polynomials in the complex plane, Results in Mathematics, 62 (2012), 415-428, DOI 10.1007/s00025-012-284-4.
  45. A.  Avdzhieva and G. Nikolov, Numerical computation of Gaussian quadrature formulae for spaces of cubic splines with equidistant knots, в: Proceedings of BGSIAM'2012, ISSN: 1314-7145, 28-39. 
  46. G. Nikolov, Inequalities of Markov-Duffin-Schaeffer type with a majorant, Sofia University "St. Kliment Ohridski", Research Excellence 2008-2013, St. Kliment Ohridski University Press,  Sofia, 2013, pp. 43-44.
  47. G. Nikolov, On Turan's inequality for ultraspherical polynomials, Ann. Univ. Sofia 101 (2013), 105-114.
  48. A. Avdzhieva and G. Nikolov, On certain asymptotically optimal quadrature formulae, в: Advanced Research in Mathematics and Computer Science (P. Sloup, K. Stefanov, I. Koychev and P. Boytchev, Eds.), St. Kliment Ohridski University Press,  Sofia, 2014, pp. 3-21.
  49. G. Nikolov, Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Rasa, J. Math. Anal. Appl. 418 (2014), 852-860.
  50. G. Nikolov and A. Shadrin, On Markov-Duffin-Schaeffer inequalities with a majorant, II, в: Constructive Theory of Functions, Sozopol 2013 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.),  Prof.  Marin Drinov Academic Publ. House, Sofia, 2014, pp. 175-197.
  51. A. Alexandrov, H. Dietert, G. Nikolov and V. Pillwein, Proof of a conjecture of M. Patrick concerning Jacobi polynomials, J. Math. Anal. Appl. 428 (2015), 750-761.
  52. G. Nikolov and V. Pillwein, An extension of Turan's inequality, Math. Inequal. Appl. 18 (1) (2015), 321-335, doi: 10.7153/mia-18-22.

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