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Article

Davydov, Oleg and Yeo, Wee Ping (2013) Refinable C2 piecewise quintic polynomials on Powell–Sabin-12 triangulations. Journal of Computational and Applied Mathematics, 240. pp. 62-73. ISSN 0377-0427

Davydov, Oleg and Prasiswa, Jennifer and Reif, Ulrich (2013) Two-stage approximation methods with extended B-splines. Mathematics of Computation, n/a (n/a). 02734-2. ISSN 0025-5718

Davydov, O. (2012) Approximation by piecewise constants on convex partitions. Journal of Approximation Theory, 164 (2). pp. 346-352. ISSN 0021-9045

Ratnarajah, N. and Simmons, A. and Davydov, Oleg and Hojjatoleslami, Ali (2012) A novel approach for improved tractography and quantitative analysis of probabilistic fibre tracking curves. Medical Image Analysis, 16. pp. 227-238. ISSN 1361-8415

Davydov, Oleg and Oanh, Dang Thi (2011) On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation. Computers and Mathematics with Applications, 62 (5). pp. 2143-2161. ISSN 0898-1221

Davydov, Oleg and Oanh, Dang Thi (2011) Adaptive meshless centres and RBF stencils for Poisson equation. Journal of Computational Physics, 230 (2). pp. 287-304. ISSN 0021-9991

Ainsworth, Mark and Andriamaro, Miangaly Gaelle and Davydov, Oleg (2011) Bernstein–Bézier finite elements of arbitrary order and optimal assembly procedures. SIAM Journal on Scientific Computing, 33 (6). pp. 3087-3109. ISSN 1064-8275

Davydov, O. and Sablonnière, P. (2010) C2 piecewise cubic quasi-interpolants on a 6-direction mesh. Journal of Approximation Theory, 162 (3). pp. 528-544. ISSN 0021-9045

Beatson, R. and Davydov, O. and Levesley, J., EPSRC (grant EP/F009615) (Funder) (2010) Error bounds for anisotropic RBF interpolation. Journal of Approximation Theory, 162 (3). pp. 512-527. ISSN 0021-9045

Davydov, Oleg and Manni, Carla (2010) A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations. Journal of Computational and Applied Mathematics, 233 (7). pp. 1674-1684. ISSN 0377-0427

Davydov, O. and Schumaker, L.L. (2008) Interpolation and scattered data fitting on manifolds using projected Powell–Sabin splines. IMA Journal of Numerical Analysis, 28 (4). pp. 785-805. ISSN 0272-4979

Davydov, Oleg and Morandi, Rossana and Sestini, Alessandra (2006) Local hybrid approximation for scattered data fitting with bivariate splines. Computer Aided Geometric Design, 23 (9). pp. 703-721.

Davydov, Oleg and Stevenson, Rob (2005) Hierarchical Riesz bases for Hs(Omega), 1 < s < 5/2. Constructive Approximation, 22 (3). pp. 365-394. ISSN 0176-4276

Davydov, O. and Zeilfelder, F. (2004) Scattered data fitting by direct extension of local polynomials to bivariate splines. Advances in Computational Mathematics, 21 (3-4). pp. 223-271. ISSN 1019-7168

Buhmann, M. D. and Davydov, O. and Goodman, T .N. T. (2003) Cubic spline prewavelets on the four-directional mesh. Foundations of Computational Mathematics, 3 (2). pp. 113-133.

Davydov, O. and Petrushev, P. (2003) Nonlinear approximation from differentiable piecewise polynomials. SIAM Journal on Mathematical Analysis, 35 (3). pp. 708-758. ISSN 0036-1410

Davydov, O. and Schumaker, L.L. (2002) Stable approximation and interpolation with C1 quartic bivariate splines. SIAM Journal on Numerical Analysis, 39 (5). pp. 1732-1748. ISSN 0036-1429

Buhmann, M.D. and Davydov, O. and Goodman, T.N.T. (2001) Box spline prewavelets of small support. Journal of Approximation Theory, 112. pp. 16-27.

Davydov, Oleg (2001) Stable local bases for multivariate spline spaces. Journal of Approximation Theory, 111 (2). pp. 267-297.

Davydov, Oleg and Schumaker, Larry L. (2001) On stable local bases for bivariate polynomial spline spaces. Constructive Approximation, 18 (1). pp. 87-116. ISSN 0176-4276

Davydov, Oleg and Nurnberger, G. and Zeilfelder, F. (2001) Bivariate spline interpolation with optimal approximation order. Constructive Approximation, 17 (2). pp. 181-208.

Book Section

Davydov, Oleg and Saeed, Abid; Boissonnat et al, J.D., ed. (2012) Stable splitting of bivariate spline spaces by Bernstein-Bézier methods. In: Curves and Surfaces. Lecture Notes in Computer Science, 6920 . Springer-Verlag, FRA, pp. 220-235. ISBN 978-3-642-27412-1

Davydov, Oleg; Georgoulis, Emmanuil H and Iske, Armin and Levesley, Jeremy, eds. (2011) Algorithms and error bounds for multivariate piecewise constant approximation. In: Approximation Algorithms for Complex Systems. Springer-Verlag, GBR, pp. 27-45. ISBN 9783642168758

Davydov, Oleg and Bohmer, Klaus; Boehmer, Klaus, ed. (2010) Smooth FEs on polyhedral domains. In: Numerical methods for nonlinear elliptic differential equations: A synopsis. Numerical Mathematics and Scientific Computation . Oxford University Press, pp. 238-250. ISBN 9780199577040

Davydov, Oleg; Cohen, Albert and Merrien, Jean-Louis and Schumaker, Larry L., eds. (2007) Error bound for radial basis interpolation in terms of a growth function. In: Curve and surface fitting. Nashboro Press, Brentwood, U.S.A., pp. 121-130. ISBN 978-0-9728482-8-2

Davydov, Oleg and Schumaker, L.L.; Martin, R. and Sabin, M. and Winkler, J., eds. (2007) Scattered data fitting on surfaces using projected Powell-Sabin splines. In: Proceedings of the 12th IMA international conference on Mathematics of surfaces XII. Springer-Verlag, pp. 138-153. ISBN 978-3-540-73842-8

Davydov, O. and Sestini, A. and Morandi, R.; Mache, Detlef H. and Szabados, József and de Bruin, Marcel G., eds. (2005) Local RBF approximation for scattered data fitting with bivariate splines. In: Trends and Applications in Constructive Approximation. International Series of Numerical Mathematics, 151 . Birkhäuser (Springer), Berlin, Germany, pp. 91-102. ISBN 3764371242

Haber, Jorg and Zeilfelder, Frank and Davydov, Oleg and Seidel, Hans-Peter; Ertl, T. and Joy, K. and Varshney, A., eds. (2001) Smooth approximation and rendering of large scattered data sets. In: Proceedings of IEEE Visualization 2001. IEEE conference on visualisation, 571 . IEEE, New York, pp. 341-347. ISBN 078037200X

Conference or Workshop Item

Ratnarajah, Nagulan and Simmons, Andrew and Davydov, Oleg and Hojjatoleslami, Ali (2010) A novel white matter fibre tracking algorithm using probabilistic tractography and average curves. In: Med Image Comput Comput Assist Interv - MICCAI 2010, 2010-09-20.

Ratnarajah, N. and Simmons, A. and Davydov, O. and Hojjat, A. (2009) An error analysis of probabilistic fibre tracking methods: average curves optimization. In: Medical Image Understanding and Analysis 2009, 2009-07-14 - 2009-07-15.