Publications:

1. R. M. Slevinsky and H. Safouhi, A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions, Numer. Algor., 92: 973–983, 2023.
   
2. R. M. Slevinsky and H. Safouhi, Compact formulae for three-center nuclear attraction integrals over exponential type functions, J. Math. Chem., 60: 1337–1355, 2022.
   
3. B. Klippenstein and R. M. Slevinsky, Fast associated classical orthogonal polynomial transforms, J. Comp. Appl. Math., 403: 113831, 2022.
   
4. S. Olver, R. M. Slevinsky and A. Townsend, Fast algorithms using orthogonal polynomials, Acta Numerica, 29: 573–699, 2020.
   
5. J. L. Aurentz and R. M. Slevinsky, On symmetrizing the ultraspherical spectral method for self-adjoint problems, J. Comp. Phys., 410: 109383, 2020.
   
6. Y. Li and R. M. Slevinsky, Fast and accurate algorithms for the computation of spherically symmetric nonlocal diffusion operators on lattices, J. Comp. Phys., 397: 108870, 2019.
   
7. R. M. Slevinsky, Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series, Appl. Comput. Harmon. Anal., 47: 585–606, 2019.
   
8. R. M. Slevinsky, H. Montanelli, and Q. Du, A spectral method for nonlocal diffusion operators on the sphere, J. Comp. Phys., 372: 893–911, 2018.
   
9. R. M. Slevinsky, On the use of Hahn's asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev–Jacobi transform, IMA J. Numer. Anal., 38: 102–124, 2018.
   
10. R. M. Slevinsky and S. Olver, A fast and well-conditioned spectral method for singular integral equations, J. Comp. Phys., 332: 290–315, 2017.
    
11. P. Gaudreau, R. M. Slevinsky and H. Safouhi, The double exponential Sinc collocation method for singular Sturm-Liouville problems, J. Math. Phys., 57: 043505-1–043505-19, 2016.
    
12. P. Gaudreau, R. M. Slevinsky and H. Safouhi, Computing energy eigenvalues of anharmonic oscillators using the double exponential Sinc collocation method, Ann. Phys., 360: 520–538, 2015.
    
13. R. M. Slevinsky and S. Olver, On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods, SIAM J. Sci. Comput., 37: A676–A700, 2015.
    
14. R. M. Slevinsky and H. Safouhi, Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation, Numer. Algor., 66: 457–477, 2014.
    
15. P. Gaudreau, R. M. Slevinsky, and H. Safouhi, An asymptotic expansion for energy eigenvalues for anharmonic oscillators, Ann. Phys., 337: 261–277, 2013.
    
16. R. M. Slevinsky and H. Safouhi, A comparative study of numerical steepest descent, extrapolation, and sequence transformation methods in computing semi-infinite integrals, Numer. Algor., 60: 315–337, 2012.
    
17. P. Gaudreau, R. M. Slevinsky, and H. Safouhi, Computation of tail probabilities via extrapolation methods and connection with rational and Padé approximants, SIAM J. Sci. Comput., 34: B65–B85, 2012.
    
18. R. M. Slevinsky and H. Safouhi, A recursive algorithm for the G transformation and accurate computation of incomplete Bessel functions, Appl. Num. Math., 60: 1411–1417, 2010.
    
19. R. M. Slevinsky, T. Temga, M. Mouattamid, and H. Safouhi, One- and two-center ETF-integrals of first order in relativistic calculation of NMR parameters, J. Phys. A: Math. Theor., 43: 225202, 2010.
    
20. R. M. Slevinsky and H. Safouhi, New formulae for higher order derivatives and applications, J. Comp. Appl. Math., 233: 405–419, 2009.
    
21. R. M. Slevinsky and H. Safouhi, The S and G transformations for computing three-center nuclear attraction integrals, Int. J. Quant. Chem., 109: 1741–1747, 2009.
    
22. R. M. Slevinsky and H. Safouhi, Numerical treatment of a twisted tail using extrapolation methods, Numer. Algor., 48: 301–316, 2008.
    

Preprints:

1. I. P. A. Papadopoulos, T. S. Gutleb, R. M. Slevinsky, and S. Olver, Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli, arXiv:2310.07541, 2023.
   
2. R. Clouâtre, B. Klippenstein, and R. M. Slevinsky, Lifting Sylvester equations: singular value decay for non-normal coefficients, arXiv:2308.11533, 2023.
   
3. R. M. Slevinsky, Fast and stable rational approximation of generalized hypergeometric functions, arXiv:2307.06221, 2023.
   
4. T. S. Gutleb, S. Olver, and R. M. Slevinsky, Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations, arXiv:2302.08448, 2023.
   
5. J. Molina and R. M. Slevinsky, A rapid and well-conditioned algorithm for the Helmholtz–Hodge decomposition of vector fields on the sphere, arXiv:1809.04555, 2018.
   
6. R. M. Slevinsky, Conquering the pre-computation in two-dimensional harmonic polynomial transforms, arXiv:1711.07866, 2017.
   

Theses:

1. [PDF] R. M. Slevinsky, New Techniques in Numerical Integration: The Computation of Molecular Integrals over Exponential-Type Functions, Ph D thesis, University of Alberta, 2014.
   
2. [PDF] R. M. Slevinsky, New Formulae for Higher Order Derivatives and a New Algorithm for Numerical Integration, M Sc thesis, University of Alberta, 2011.
   

Software:

• ApproxFun.jl, a Julia package for function approximation.
  
• DEQuadrature.jl, a Julia package for high-precision quadrature.
  
• FastTransforms, a C library for fast orthogonal polynomial transforms.
  
• FastTransforms.jl, a Julia package for fast orthogonal polynomial transforms.
  
• HypergeometricFunctions.jl, a Julia package for calculating hypergeometric functions.
  
• SingularIntegralEquations.jl, a Julia package for solving singular integral equations and Riemann–Hilbert problems.
  

Presentations:

• Fast harmonic polynomial transforms, Computational Methods in Analytics, Inference, and Computation in Cosmology, Institut Henri Poincaré, Paris, France, 2018.
  
• Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series, The 14^th International Symposium on Orthogonal Polynomials, Special Functions and Applications, University of Kent, Canterbury, UK, 2017.
  
• A fast and well-conditioned spectral method for singular integral equations, The 8^th International Congress on Industrial and Applied Mathematics, Beijing, China, 2015.
  
• On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods, Numerical analysis seminar, The University of Tokyo, 2015.
  
• A Constant 3-fold Autoconvolution, NA group internal seminar, University of Oxford, 2015.