List of publications

  1. T. Sanders, R.B. Platte. Multiscale Higher Order TV Operators for l1 Regularization and Their Relationship to Daubechies Wavelets. Appl. Comput. Harmon. Anal., (submitted).
  2. B. Adcock, R. Archibald, A. Gelb, R.B. Platte, G. Song, E.G. Walsh. Parameter Assessment from Time-Dependent MR Signals Using Sequential Imaging. IEEE T. Med. Imaging, (submitted).
  3. T. Sanders, A. Gelb, R.B. Platte. Composite SAR Imaging Using Sequential Joint Sparsity. J. Comput. Phys., (submitted).
  4. T. Sanders, A. Gelb, R.B. Platte, I. Arslan, K. Landskron. Recovering Fine Details from Under-Resolved Electron Tomography Data using Higher Order Total Variation l1 Regularization. Ultramicroscopy, 174 (2017) 97-105. (pdf)
  5. B. Adcock, R.B. Platte. A mapped polynomial method for high-accuracy approximations on arbitrary grids. SIAM J. Numer. Anal. 54 (2016) 2256-2281. (pdf)
  6. J.M. Martel, R.B. Platte. Stability of radial basis function methods for convection problems on the circle and sphere. J. Sci. Comput. 69 (2016) 487-505. (pdf)
  7. R. Archibald, A. Gelb, R.B. Platte. Image reconstruction from undersampled Fourier data using the polynomial annihilation transform. J. Sci. Comput. 67 (2016) 432-452. (pdf)
  8. R.B. Platte. A windowed Fourier method for approximation of non-periodic functions on equispaced nodes. In R.M. Kirby et al. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 , Lecture Notes in Computational Science and Engineering, 106, Springer International Publishing (2016) 405-413. (pdf)
  9. R.B. Platte. $C^\infty$ compactly supported and positive definite radial kernels. SIAM J. Sci. Comput. 37 (2015) A1934-A1956. (pdf)
  10. A.A. Mitrano, R.B. Platte. A numerical study of divergence-free kernel approximations. Appl. Numer. Math., 96 (2015) 94–107. (pdf)
  11. R.B. Platte, A.J. Gutierrez, A. Gelb. Fourier reconstruction of univariate piecewise-smooth functions from non-uniform spectral data with exponential convergence rates. Appl. Comput. Harmon. Anal., 39 (2015) 427-449. doi:10.1016/j.acha.2014.10.002 (pdf)
  12. K. McLeod. Fourfun: a new system for automatic computations using Fourier expansions. R.B. Platte advisor. SIAM Undergraduate Research Online (SIURO), 7 (2014) 330-351. (pdf)
  13. R.B. Platte. How fast do radial basis function interpolants of analytic functions converge? IMA J. Numer. Anal. 31 (2011) 1578-1597. (pdf)
  14. R.B. Platte, L.N. Trefethen, A.B.J. Kuijlaars. Impossibility of fast stable approximation of analytic functions from equispaced samples. SIAM Rev. 53 (2011) 308-318. (pdf)
  15. J. Holmer, R.B. Platte, S. Roudenko. Blow-up criteria for the 3D cubic nonlinear Schrödinger equation. Nonlinearity 23 (2010) 977-1030. doi:10.1088/0951-7715/23/4/011
  16. R.B. Platte, L.N. Trefethen. Chebfun: a new kind of numerical computing, in A. D. Fitt et al., Progress in Industrial Mathematics at ECMI 2008. Springer (2010) 69-87. (pdf)
  17. R. Pachón, R.B. Platte, L.N. Trefethen. Piecewise smooth chebfuns. IMA J. Numer. Anal. 30 (2010) 898-916. (pdf)
  18. R.B. Platte, A. Gelb. A hybrid Fourier-Chebyshev method for partial differential equations. J. Sci. Comput. 39 (2009) 244-264. (pdf)
  19. R.B. Platte, L.F. Rossi, T. Mitchell. Using global interpolation to evaluate the Biot-Savart integral for deformable elliptical Gaussian vortex elements. SIAM J. Sci. Comput. 31 (2009) 2342-2360. (pdf)
  20. A. Gelb, R.B. Platte, W.S. Rosenthal. The discrete orthogonal polynomial least squares method for approximation and solving partial differential equations. Commun. Comput. Phys. 3 (2008) 734-758. (pdf)
  21. R.B. Platte, T.A. Driscoll. Eigenvalue stability of radial basis function discretizations for time-dependent problems. Computers Math. Applic. 51 (2006) 1251-1268. (pdf)
  22. R.B. Platte, T.A. Driscoll. Polynomials and potential theory for Gaussian radial basis function interpolation. SIAM J. Numer. Anal. 43 (2005) 750-766. (pdf)
  23. R.B. Platte. Accuracy and Stability of Global Radial Basis Function Methods for the Numerical Solution of Partial Differential Equations. Ph.D. Thesis, University of Delaware, 2005. (pdf)
  24. R.B. Platte, T.A. Driscoll. Computing eigenmodes of elliptic operators using radial basis functions. Computers Math. Applic. 48 (2004) 561-576. (pdf)
  25. J.R. Claeyssen, R.B. Platte, E. Bravo. Simulation in primitive variables of incompressible flow with pressure Neumann condition. Int. J. for Numer. Meth. Fluids 30 (1999) 1009-1026. (pdf)
  26. E. Bravo, J.R. Claeyssen, R.B. Platte. A direct one-step pressure actualization for incompressible flow with pressure Neumann condition. J. Comput. Appl. Math. 103 (1999) 43-53.