Publications

Number of Publications:

List of Publications

    MONOGRAPHS:

  1. Methods of Spline Functions, Nauka, Moscow, 1980, 352 pp. (with Yu.S. Zav'yalov and V.L. Miroshnichenko).
  2. Methods of Shape-Preserving Spline Approximation, World Scientific Publ. Co. Pte. Ltd., Singapore, 2000, xvi+338 pp.
  3. Methods of Isogeometric Spline Approximation, Regular and Chaotic Dynamics, Moscow-Izhevsk, 2006, 416 pp.
  4. Methods of Isogeometric Spline Approximation. Second edition. Fizmatlit, Moscow, 2006, 360 pp.
  1. Laurent, P.J., Approximation et Optimisation, 1975, 496 pp.
  2. Descloux, J., Methode des Elements Finis, 1976, 96 pp.
  3. Ciarlet, Ph., The Finite Element Method for Elliptic Problems, 1980, 512 pp.
  4. Zienkiewicz, O.C. and K. Morgan, Finite Elements and Approximation, 1986, 320 pp.
  1. Approximation Theory and Problems of Computational Mathematics, Modelirovanie v Mekhanike, special issue, Novosibirsk, 5(22) (1991) No. 5.

    LECTURE NOTES:

  1. Cubic Spline Functions, Novosobirsk State University Press, Novosibirsk, 1998, 28 pp.
  2. Isogeometric Spline Approximation, Novosobirsk State University Press, Novosibirsk, 1998, 152 pp.
  3. Approximation by Lagrange Splines, Novosobirsk State University Press, Novosibirsk, 1999, 36 pp.
  4. Lagrange Polynomials and Lagrange Splines, Novosobirsk State University Press, Novosibirsk, 2004, 40 pp.
  5. Interpolation by Cubic and Bicubic Splines, Novosobirsk State University Press, Novosibirsk, 2004, 40 pp.
  6. Monotone and Convex Spline Interpolation, Novosobirsk State University Press, Novosibirsk, 2004, 40 pp.
  7. Difference Methods for Constructing Shape Preserving Splines, Novosobirsk State University Press, Novosibirsk, 2004, 48 pp.
  8. Smoothing by Cubic Splines, Novosobirsk State University Press, Novosibirsk, 2005, 32 pp.

    THESES AND SYNOPSES OF THESES:

  1. On the exact solution of a difference analog of the Dirichlet problem of high-order accuracy for the polyharmonic equation, M.Sc. Thesis, Novosibirsk State University, Novosibirsk, 1969, 78 pp.
  2. Certain questions of the theory and applications of spline functions, Synopsis of Ph.D. Thesis, Novosibirsk State University, Novosibirsk, 1973, 8 pp.
  3. Certain questions of the theory and applications of spline functions, Ph.D. Thesis, Novosibirsk State University, Novosibirsk, 1973, 101 pp.
  4. Methods of shape-preserving spline approximation, Synopsis of D.Sc. Thesis, Institute of Computational Technologies, Russian Academy of Sciences, Novosibirsk, 1997, 34 pp.
  5. Methods of shape-preserving spline approximation, D.Sc. Thesis, Institute of Computational Technologies, Russian Academy of Sciences, Novosibirsk, 1997, 256 pp.

    PAPERS IN REFEREED JOURNALS AND CONFERENCE PROCEEDINGS:

  1. On the exact solution of a difference analog of the Dirichlet problem of high-order accuracy for the polyharmonic equation, in: Questions of Exactness and Efficiency of Computational Algorithms, Kiev, 1969, 131-148 (with N.N. Yanenko and A.N. Valiullin).
  2. Iteration processes for exact solution of the difference Dirichlet problem of high-order exactness, in: Numerical Methods for Solution of Problems in Elasticity and Plasticity Theory, Novosibirsk, 1969, 129-142 (with N.N. Yanenko and A.N. Valiullin).
  3. On a question of boundary condition analysis and about a difference scheme of high-order accuracy for the harmonic equation, in: Chislennye Metody v Mekhanike Vyazkoy Zhidkosti, Novosibirsk, 1969, 28-33 (with A.N. Valiullin).
  4. An iteration method for the construction of polycubic spline functions, Chislennye Metody Mekhaniki Sploshnykh Sred 1 (1970), No. 3, 84-89 (with N.N. Yanenko).
  5. An iteration method for the construction of polycubic spline functions, Chislennye Metody Mekhaniki Sploshnykh Sred 1 (1970), No. 3, 84-89 (with N.N. Yanenko).
  6. Construction of L-splines, Chislennye Metody Mekhaniki Sploshnykh Sred 3 (1972), No. 3, 64-71.
  7. Obtaining splines by averaging piecewise-constant functions. Splines with supplementary nodes, Chislennye Metody Mekhaniki Sploshnykh Sred 4 (1973), No. 1, 39-55.
  8. On an iterative method of spline construction, Variatsionno-Raznostnye Metody v Matematicheskoi Fizike, Novosibirsk, Computing Center, Siberian Branch of USSR Academy of Sciences, 1974, 107-115.
  9. Certain properties of cubic Hermite splines with supplementary nodes, Doklady Akademii Nauk SSSR 217 (1974), No. 5, 1007-1010 (with V.V. Kobkov). (Translated as Soviet Math. Dokl. 15 (1975), No. 4, 1162-1166).
  10. Splines with supplementary nodes II. Limits and properties, Chislennye Metody Mekhaniki Sploshnykh Sred 5 (1974), No. 4, 48-70 (with V.V. Kobkov).
  11. Interpolation splines of first degree, Metody Splain-Funktsiy. Vychislitelnye Sistemy 1975, No. 65, 50-59, 161-162.
  12. Spline solution of a mixed Lagrange-Hermite problem, Chislennye Metody Mekhaniki Sploshnykh Sred 8 (1977), No. 1, 59-82.
  13. On boundary conditions in the case of interpolation by parabolic splines, Vychislitelnye Sistemy 1981, No. 87, 11-17.
  14. On the realization of interpolation by parabolic splines, Chislennye Metody Mekhaniki Sploshnykh Sred 13 (1982), No. 4, 35-51.
  15. An application of parabolic B-splines for solving interpolation problems, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki 23 (1983), No. 2, 278-289. (Translated as USSR Comput. Maths Math. Phys. 23 (1983), No. 2, 13-19).
  16. Numerical differentiation and integration on basis of interpolational parabolic splines, Chislennye Metody Mekhaniki Sploshnykh Sred 14 (1983), No. 2, 68-80.
  17. Numerical differentiation on basis of discrete cubic splines, Chislennye Metody Mekhaniki Sploshnykh Sred 14 (1983), No. 4, 84-96.
  18. Parabolic X-splines, Vychislitelnye Sistemy 1983, No. 98, 3-19, 151.
  19. On an interpolation method of discontinuous functions, Vychislitelnye Sistemy 1983, No. 98, 20-26, 151.
  20. Interpolation by parabolic Hermite splines, Izvestiya Vysshikh Uchebnykh Zavedeniy. Matematika 1984, No. 5, 25-32. (Translated as Sov. Math. 28 (1984), No. 5, 29-37).
  21. Estimates of approximation exactness for functions of one real variable by using parabolic Hermite splines, Modelirovanie i Optimizatsiya Strukturnykh System, Barnaul, 1984, 30-39.
  22. Interpolation by means of discrete parabolic splines, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki 24 (1984), No. 5, 640-649. (Translated as USSR Comp. Maths Math. Phys. 24 (1984), 9-15).
  23. Discrete quadratic splines, Chyslennye Metody Mekhaniki Sploshnykh Sred 15 (1984), No. 6, 94-109.
  24. Interpolation by rational parabolic splines, Chislennye Methody Mekhaniki Sploshnykh Sred 15 (1984), No. 4, 60-70.
  25. Continuation of network solutions of equations with discontinuous coefficients by parabolic splines, Variational-Difference Methods in Mathematical Physics. Collection of scientific works, Moscow, Vol. 2, 1984, 144-150.
  26. Review of the book by O. Zienkiewicz and K. Morgan, Finite Elements and Approximation, Zhurnal Novye knigy za Rubezhom, 1984, Ser. A, No. 4, Mir, Moscow, 61-64.
  27. On boundary conditions in the case of interpolation by parabolic splines on a nonuniform network, Vychislitelnye Sistemy 1986, No. 115, 60-71.
  28. Isogeometric interpolation by rational splines, Approksimatsiya Splainami. Vychislitelnye Sistemy 1987, No. 121, 11-36, 125 (with S.A. Yatsenko).
  29. Conservative interpolation by rational splines, in: Approximation Theory VI, C.K. Chui, L.L. Schumaker and J.D. Ward (eds.), Academic Press, Boston, 1989, 365-367 (with S.A. Yatsenko).
  30. Three-dimensional isogeometric approximation by rational B-splines, in: Proceedings of the Conference on Theoretical Foundations and Construction of Numerical Algorithms for a Solution of Mathematical Physics Problems, Krasnovidovo, USSR, October 15-19, Keldysh Institute of Applied Mathematics, Moscow, 1991, p. 112-116 (with S.A. Yatsenko).
  31. On parametrization choices for cubic splines, Modelirovanie v Mekhanike 5 (22) (1991), No. 5, 118-135 (with S.A.~Yatsenko).
  32. Rational B-splines and algorithms of isogeometric local approximation, Russian Journal of Numerical Analysis and Mathematical Modelling 8 (1993), No. 6, 481-504 (with L.A. Vanin).
  33. Polynomial splines, Computational Technologies, Novosibirsk 3 (1994), No. 9, 71-107.
  34. Algorithms and program package for isogeometric approximation by generalized splines, Computational Technologies, Novosibirsk 4 (1995), No. 1, 219-232.
  35. Construction of generalized B-splines and their properties, Doklady Rossiyskoi Akademii Nauk 341 (1995), No. 6, 744-748.
  36. Local bases for generalized cubic splines, Russian Journal of Numerical Analysis and Mathematical Modelling 10 (1995), No. 1, 49-80.
  37. Isogeometric interpolation by generalized splines, Russian Journal of Numerical Analysis and Mathematical Modelling 11 (1996), No. 3, 223-246.
  38. Shape-preserving spline approximation via local algorithms, in: Advanced Topics in Multivariate Approximation, F. Fontanella, K. Jetter and P.J. Laurent (eds.), pp. 181-196, World Scientific Publishing Co. Inc., Singapore, 1996.
  39. GB-splines and their properties, Annals of Numerical Mathematics 3 (1996), 139-149.
  40. Generalized B-splines and algorithms of shape-preserving approximation, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki 36 (1996), No. 12, 3-22. (Translated as Comp. Maths Math. Phys. 36 (1996), No. 12, 1637-1653).
  41. On tension spline construction by difference method, in: Proceedings of the Int. Conference on Computational Mathematics, Chulalongkorn University, Bangkok, ISBN 974-637-467-2, 1997, pp. 204-211.
  42. Generalized tension B-splines, in: Curves and Surfaces with Applications in CAGD. A. Le Me'haute', C. Rabut, and L.L. Schumaker (eds.), Vanderbilt Univ. Press, Nashville, TN, ISBN 0-8265-1293-3, 1997, pp. 247-254 (with P. Sattayatham).
  43. Shape-preserving C2 spline interpolation, in: Proceedings of the Second Asian Mathematical Conference 1995, S. Tangmanee and E. Schulz (eds.), World Scientific Publishing Co. Pte. Ltd., Singapore, ISBN 981-02-3225-X, 1998, pp. 430-438.
  44. A general approach to discrete generalized splines, in: Proceedings of the Third Annual National Symposium on Computational Science and Engineering, Chulalongkorn University, March 24-26, 1999, pp. 283--292.
  45. GB-splines of arbitrary order, Journal of Computational and Applied Mathematics 104 (1999), 63-88 (with P. Sattayatham).
  46. On discrete hyperbolic tension splines, Advances in Computational Mathematics 11 (1999), 331-354 (with P. Costantini and C. Manni).
  47. Approximation by Lagrange splines, in: Proceedings of the Fourth Annual National Symposium on Computational Science and Engineering, Kasetsart University, March 27-29, 2000, pp. 306-315 (with A. Luadsong).
  48. Algorithms for shape-preserving local approximation with automatic selection of tension parameters, Computer Aided Geometric Design 17 (2000), 17-37.
  49. On discrete GB-splines, Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM J.) 42 (E), 2000, pp. C877-C899.
  50. Difference method for constructing shape-preserving splines, in: Proceedings of the Fifth Annual National Symposium on Computational Science and Engineering, Kasetsart University, June 18-20, 2001, pp. 390-397 (with A. Luadsong).
  51. Approximation by discrete GB-splines, Int. J. Numerical Algorithms 27(2) : 169-188, June 2001.
  52. Discrete GB-splines and their properties, in: Approximation Theory X: Wavelets, Splines, and Applications, Charles K. Chui, Larry L. Schumaker, and Joachim Stöckler (eds.), Vanderbilt University Press, Nashville, TN, USA, ISBN 0-8265-1416-2, 2002, pp. 355-368.
  53. On interpolating thin plate tension splines, in: Curve and Surface Fitting: Saint-Malo 2002, A. Cohen, J.-L. Merrien, and L.L. Schumaker (eds.), Nashboro Press, Brentwood, USA, 2003, pp. 239-248.
  54. Interpolation by shape preserving biharmonic splines,Computational Technologies, Vol. 10, N 1, 2005, pp. 49-57.
  55. DMBVP for tension splines, in: Proceedings of the International Conference on Applied Mathematics and Scientific Computing,, Springer, 2005. Netherlands, ISBN 1-4020-3196-3 (ISBN 1-4020-3197-1 e-book), pp. 67-93.

    PREPRINTS:

  1. Interpolation by quadratic splines, Preprint No. 3, Institute of Theoretical and Applied Mechanics, Siberian Branch of USSR Academy of Sciences, Novosibirsk, 1981, 61 pp.
  2. Discrete interpolating parabolic splines and their application to the problem of numerical differentiation, Preprint No. 97, Computing Center, Siberian Branch of USSR Academy of Sciences, Novosibirsk, 1982, 27 pp.
  3. Approximation estimates for interpolating parabolic splines, Preprint No. 2-84, Institute of Theoretical and Applied Mechanics, Siberian Branch of USSR Academy of Sciences, Novosibirsk, 1984, 24 pp.
  4. Solution of isogeometric interpolation problems in a class of rational splines, Preprint No. 3-88, Institute of Theoretical and Applied Mechanics, Siberian Branch of USSR Academy of Sciences, Novosibirsk, 1988, 60 pp. (with S.A. Yatsenko).
  5. Algorithms of isogeometric approximation by rational splines, Preprint No. 9-90, Institute of Theoretical and Applied Mechanics, Siberian Branch of USSR Academy of Sciences, Novosibirsk, 1990, 35 pp. (with S.A. Yatsenko).
  6. Difference methods for constructing hyperbolic tension splines, Rapporto Interno 341/1998, Universita' di Siena, 22 pp. (with P. Costantini and C. Manni).

    PAPERS SUBMITTED FOR PUBLICATION:

  1. Mesh methods for hyperbolic spline tabulation, to appear in: Siberian J. of Comp. Math., Novosibirsk, 21 pp.
  2. On constructing interpolation hyperbolic splines, to appear in: J. of Comp. Math. and Math. Physics, Moscow, 2008. V. 48. N 4. P. 34-44.
  3. Parallel calculations by constructing interpolation hyperbolic splines, to appear in: Proceedings of the fourth siberian school-seminar on parallel and high-performing calculations, Tomsk, Tomsk State University Press. 2008. 10 pp.

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