Oleg Davydov's Publications: 1995-2010

Oleg Davydov's Publications: 1995-2010

A new version of quantitative resonance principle and applications: Summary, Dnepropetrovsk, 1994. PDF

A class of weak Chebyshev spaces and characterization of best approximations, J. Approx. Theory 81 (1995), 250-259.

Note on the approximation of functions in Lipschitz spaces, East J. Approx. 1 (1995), 349-356.

Snake theorem for weak Descartes systems, Ukrain. Mat. Zh. 47 (1995), 315-321 [in Russian]; English translation in Ukrainian Math. J. 47 (1995), 369-375.

Characterization of the best uniform approximation of periodic functions by convex classes defined by strictly CVD kernels, in "Approximation Theory VIII" (C.K.Chui and L.L.Schumaker, Eds.), Vol. 1: "Approximation and Interpolation," pp. 177-184, World Scientific Publishing Co., 1995.

Sequences of rectangular Fourier sums of continuous functions with given majorants of the mixed moduli of smoothness, Mat. Sb. 187 (1996), no.7, 35-58 [in Russian]; English translation in Russian Acad. Sci. Sb. Math. 187 (1996), 981-1004.

(with A.Pinkus) Best approximation and cyclic variation diminishing kernels, J.Approx. Theory 89 (1997), 380-423.

On almost interpolation, J. Approx. Theory 91 (1997), 398-418.

(with M.Sommer and H.Strauss) On almost interpolation by multivariate splines, in "Multivariate Approximation and Splines" (G.Nürnberger, J.W.Schmidt and G.Walz, Eds.), pp. 45-58, ISNM, Birkhäuser, 1997.

(with M.Sommer and H.Strauss) Locally linearly independent systems and almost interpolation, in "Multivariate Approximation and Splines" (G.Nürnberger, J.W.Schmidt and G.Walz, Eds.), pp. 59-72, ISNM, Birkhäuser, 1997.

(with G.Nürnberger, G.Walz and F.Zeilfelder) Interpolation by bivariate splines on crosscut partitions, in "Multivariate Approximation and Splines" (G.Nürnberger, J.W.Schmidt and G.Walz, Eds.), pp. 189-203, ISNM, Birkhäuser, 1997.

(with G. Nürnberger and F. Zeilfelder) Approximation order of bivariate spline interpolation for arbitrary smoothness, J. Comput. Appl. Math. 90 (1998), 117-134.

Appendix to "Best approximation by periodic smooth functions" (by J.A.Oram), J. Approx. Theory 92 (1998), 159-166.

Locally linearly independent basis for $C^1$ bivariate splines of degree $q\ge 5$, in "Mathematical Methods for Curves and Surfaces II" (M.Daehlen, T.Lyche, L.L.Schumaker, Eds.), pp. 71-78, Vanderbilt University Press, 1998.

(with G.Nürnberger and F.Zeilfelder) Interpolation by cubic splines on triangulations, in "Approximation Theory IX" (C.K.Chui and L.L.Schumaker, Eds.), Vol.2: "Computational Aspects", pp. 17-24, Vanderbilt University Press, 1998.

(with M.Sommer) Interpolation and almost interpolation by weak Chebyshev spaces, in "Approximation Theory IX" (C.K.Chui and L.L.Schumaker, Eds.), Vol.2: "Computational Aspects", pp. 25-32, Vanderbilt University Press, 1998.

(with M.Sommer and H.Strauss) On almost interpolation and locally linearly independent bases, East J. Approx. 5 (1999), 67-88.

(with G.Nürnberger and F.Zeilfelder) Interpolation by splines on triangulations, in "New Developments in Approximation Theory (IDoMAT 98)" (M.D. Buhmann, M.Felten, D.H. Mache and M.W. Müller, Eds.), pp. 49-70, ISNM 132, Birkhäuser, 1999.

(with M.Sommer) Interpolation by weak Chebyshev spaces, J. Approx. Theory 102 (2000), 243-262.

(with M. Sommer and H. Strauss) Interpolation by bivariate linear splines, J. Comput. Appl. Math. 119 (2000), 115-131.

(with G.Nürnberger and F.Zeilfelder) Cubic spline interpolation on nested polygon triangulations, in "Curve and Surface Fitting: Saint-Malo 1999" (A. Cohen, C. Rabut, and L. L. Schumaker, Eds.), pp. 161-170, Vanderbilt University Press, 2000.

(with L. L. Schumaker) Stable local nodal bases for $C^1$ bivariate polynomial splines, in "Curve and Surface Fitting: Saint-Malo 1999" (A. Cohen, C. Rabut, and L. L. Schumaker, Eds.), pp. 171-180, Vanderbilt University Press, 2000.

(with G.Nürnberger) Interpolation by $C^1$ splines of degree $q\ge4$ on triangulations, J. Comput. Appl. Math.126 (2000), 159-183.

(with L. L. Schumaker) Locally linearly independent bases for bivariate polynomial spline spaces, Advances in Comp. Math.13 (2000), 355-373.

(with G.Nürnberger and F.Zeilfelder) Bivariate spline interpolation with optimal approximation order, Constr. Approx.17 (2001), 181-208.

(with M. D. Buhmann and T. N. T. Goodman) Box spline prewavelets of small support, J. Approx. Theory 112 (2001), 16-27.

Stable local bases for multivariate spline spaces, J. Approx. Theory 111 (2001), 267-297.

On the computation of stable local bases for bivariate polynomial splines, in "Trends in Approximation Theory" (K.Kopotun, T.Lyche, and M.Neamtu, Eds.), pp. 85-94, Vanderbilt University Press, 2001.

(with J. Haber, F. Zeilfelder and H.-P. Seidel) Smooth approximation and rendering of large scattered data sets, in ''Proceedings of IEEE Visualization 2001,'' (Th.Ertl, K.Joy and A.Varshney, Eds.), pp.341-347, 571, IEEE Computer Society, 2001.

(with L. L. Schumaker) On stable local bases for bivariate polynomial spline spaces, Constr. Approx. 18 (2002), 87-116.

(with L. L. Schumaker) Stable approximation and interpolation with C^1 quartic bivariate splines, SIAM J. Numer. Anal. 39 (2002), 1732-1748.

On local refinement of smooth finite elements and splines, Mat. Model.14 (2002), no.5, 109-116.

On the approximation power of local least squares polynomials, in "Algorithms for Approximation IV," (J.Levesley, I.J.Anderson and J.C.Mason, Eds.), pp.346-353, University of Huddersfield, UK, 2002.

Locally stable spline bases on nested triangulations, in "Approximation Theory X: Wavelets, Splines, and Applications," (C.K.Chui, L.L.Schumaker, and J.Stöckler, Eds.), pp.231-240, Vanderbilt University Press, 2002.

(with M. D. Buhmann and T. N. T. Goodman) Cubic spline prewavelets on the four-directional mesh, Found. Comp. Math. 3 (2003), 113-133.

(with P. Petrushev) Nonlinear approximation from differentiable piecewise polynomials, SIAM J. Math. Anal. 35 (2003), 708--758.

(with F. Zeilfelder) Scattered data fitting by direct extension of local polynomials to bivariate splines, Advances in Comp. Math. 21 (2004), 223-271.

(with R. Stevenson) Hierarchical Riesz Bases for H^s(\Omega), 1 < s < 5/2, Constr. Approx. 43 (2005), 365-394.

(with A. Sestini and R. Morandi) Local RBF approximation for scattered data fitting with bivariate splines, in "Trends and Applications in Constructive Approximation," (M. G. de Bruin, D. H. Mache, and J.Szabados, Eds.), pp.91--102, ISNM Vol.151, Birkhäuser, 2005.

(with R. Morandi and A. Sestini) Local hybrid approximation for scattered data fitting with bivariate splines, Comput. Aided Geom. Design 23 (2006), 703-721.

(with L. L. Schumaker) Scattered data fitting on surfaces using projected Powell-Sabin splines, in "Mathematics of Surfaces 2007," (R. Martin, M. Sabin, and J. Winkler, Eds.), pp.~138--153, LNCS 4647, Springer-Verlag, 2007.

Error bound for radial basis interpolation in terms of a growth function, in "Curve and Surface Fitting: Avignon 2006," (A. Cohen, J.-L. Merrien and L. L. Schumaker, Eds.), pp. 121-130, Nashboro Press, Brentwood, 2007.

Smooth finite elements and stable splitting, Berichte "Reihe Mathematik" der Philipps-Universität Marburg, 2007-4. An adapted version of this article has appeared as Section 4.2.6 "Smooth FEs on polyhedral domains" of the book K. Böhmer, Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis, Oxford University Press, Oxford, 2010.

(with L. L. Schumaker) Interpolation and scattered data fitting on manifolds using projected Powell-Sabin splines, IMA J. Numer. Anal., 28 (2008), 785--805.

(with N. Ratnarajah, A. Simmons and A. Hojjat) An error analysis of probabilistic fibre tracking methods: average curves optimization, in ``Medical Image Understanding and Analysis 2009,'' (Jamshid Dehmeshki, Andreas Hoppe and Darrel Greenhill, Eds.) Kingston University, London, 2009, pp.~134--138.

(with C. Manni) A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations, J. Comput. Appl. Math., 233 (2010), pp. 1674-1684.

(with R. Beatson and J. Levesley) Error bounds for anisotropic RBF interpolation, J. Approx. Theory, 162 (2010), 512-527.

(with P. Sablonnière) C2 piecewise cubic quasi-interpolants on a 6-direction mesh, J. Approx. Theory, 162 (2010), 528-544.

(with N. Ratnarajah, A. Simmons and A. Hojjat) A novel white matter fibre tracking algorithm using probabilistic tractography and average curves, in "Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2010" (T. Jiang, N. Navab, J. P. W. Pluim and M. A. Viergever, Eds.), pp. 666-673, LNCS 6361, Springer-Verlag, 2010.