Recent publications

Here are number of recent publications which you can download from the links

  • S. Hubbert and J. Levesley, Convergence of multilevel stationary Gaussian quasi-interpolation. https://arxiv.org/pdf/1609.02457.pdf
  • S. Hubbert and J. Levesley, Convergence of multilevel Gaussian convolution, submitted. https://arxiv.org/abs/1711.10803
  • N. Kamis, F. Chiclana, Preference Similarity Network Structural Equivalence Consensus based Group Decision Making Model, Soft Computing. https://doi.org/10.1016/j.asoc.2017.11.022
  • Y. Zhao, Q. Zhang, and J. Levesley, Multilevel sparse grids collocation for linear partial differential equations, with tensor product smooth basis functions, Computers and Mathematics with Applications, doi 10.1016/j.camwa.2017.10.014. https://arxiv.org/pdf/1710.07023.pdf
  • E. Mirkes, A. Gorban, J. Levesley, P. Elkington, and J. Whetton, Pseudo-outcrop Visualization of Borehole Images and Core Scans, Mathematical Geosciences 2017, 10.1007/s11004-017-9701-2: https://arxiv.org/pdf/1702.02633.pdf

  • Zhang, Q., Zhao, Y. & Levesley J, Adaptive radial basis function interpolation using an error indicator, Numer Algor (2017). doi:10.1007/s11075-017-0265-5: error-indicator.pdf

  • Usta, F & Levesley J, Multilevel quasi-interpolation on a sparse grid with the Gaussian, Numer Algor (2017). doi:10.1007/s11075-017-0340-y:multilevelquasi.pdf

  • Mirkes, E., Coats, T., Levesley, J., and Gorban, A., Handling missing data in large healthcare dataset: a case study of unknown trauma outcomes” Computers in Biology and Medicine 75 (2016) 203–216:MirkesCoatsLevesleygorban2016.pdf

  • Goldobin, D. S.; Pimenova, A. V.; Levesley, J.; Elkington, P.; Bacciarelli, M. Noise-produced patterns in images constructed from magnetic flux leakage data. Math. Model. Nat. Phenom. 10 (2015), no. 3, 139–148.

  • Pimenova, A. V.; Goldobin, D. S.; Levesley, J.; Ivantsov, A. O.; Elkington, P.; Bacciarelli, M. Magnetic flux leakage method: large-scale approximation. Math. Model. Nat. Phenom. 10 (2015), no. 3, 61–70.

  • Georgoulis, E. H.; Levesley, J.; Subhan, F. Multilevel sparse kernel-based interpolation using conditionally positive definite radial basis functions. Numerical mathematics and advanced applications 2011, 157–164, Springer, Heidelberg, 2013.

  • On the density of polyharmonic splines, with Thomas Hangelbroek, Journal of Approximation Theory 167 (2013) 94–108. http://www.sciencedirect.com/science/journal/00219045

  • A multiplier version of the Bernstein inequality on the complex sphere, with A. K. Kushpel, Journal of Computational and Applied Mathematics 240 (2013), 184--191. http://www.sciencedirect.com/science/article/pii/S0377042712004074

  • Georgoulis, Emmanuil H.; Levesley, Jeremy; Subhan, Fazli Multilevel sparse kernel-based interpolation. SIAM J. Sci. Comput. 35 (2013), no. 2, A815–A831. http://arxiv.org/abs/1204.4153v1
  • Fast, stable interpolation of well data using the norm function, to appear in Approximation Algorithms for Complex Systems, Springer 2011. wellinterp.pdf
  • Error bounds for anisotropic RBF interpolation, with Rick Beatson and Oleg Davydov, Error bounds for anisotropic RBF interpolation. Journal of Approximation Theory 162(3): 512-527 (2010); aniso.pdf
  • Energies, group-invariant kernels and numerical integration on compact manifolds,  with S.B. Damelin,  D.L. Ragozin, X. Sun, Journal of Complexity25 (2009), 152-162; energy.pdf
  • Stable simulation of fluid flow with high Reynolds' number using Ehrenfests' steps, Numerical Algorithms 45 (2007), 389-408.
  • Radial basis interpolation on homogeneous manifolds: convergence rates, Adv. in Comp. Math. 27 (2007), 237-246; published online at SpringerLink ; manifolds.pdf
  • Extending the range of error estimates for radial approximation in Euclidean space and on spheres, with R. A. Brownlee and E. H. Georgoulis, SIAM J. Math. Anal. 39 (2007), 554-564; extended.pdf
  • Stability and stabilisation of the lattice Boltzmann method: Magic steps and salvation operations, with R. A. Brownlee and A. N. Gorban, Phys. Rev. E 75 (2007); magic.pdf
  • Stabilisation of the lattice Boltzmann method using the Ehrenfests' coarse-graining idea ; with R. A. Brownlee and A. N. Gorban, Phys. Rev. E, 137 (2006); lbmes.pdf
  • Estimates of n-widths of Besov classes on two-point homogeneous manifolds; with A. K. Kushpel and S. Tozoni, Math. Nachr 282 (2009), 1-16; besov.pdf
  • Perturbed kernel approximation on homogeneous manifolds; with X. Sun,Journal of Computational and Applied Mathematics 199 (2007), 159-171 ; perturbed.pdf
  • Embeddings of Beppo-Levi spaces in Holder-Zygmund spaces, and a new method for radial basis function interpolation error estimates; with R. K. Beatson and H.-Q. Bui, Journal of Approximation Theory 137 (2006), 166-178; embed.pdf
  • Approximation in rough native spaces by shifts of smooth kernels on spheres ; with X. Sun, Journal of Approximation Theory 133 (2005), 269-283; rough.pdf

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