Richard Slevinsky

Profile

Select Publications

Name: Richard Slevinsky

Position Title: Associate Professor

Office Phone Number: (204) 474-6647

Email: Richard.Slevinsky@umanitoba.ca

Research and Teaching Interests

Numerical analysis, scientific computing, spectral methods for differential and integral equations, fast orthogonal polynomial transforms

Education

B.Sc. University of Alberta
M.Sc. University of Alberta
Ph.D. University of Alberta

Current graduate students

Ikaro Penha Costa (M.Sc. Thesis)
Brock Klippenstein (M.Sc. Thesis)
Yu Li (M.Sc. Thesis)

Former graduate students

Emmanuel Appiah-Kubi (M.Sc. Thesis)

Courses taught

MATH 1700 Calculus 2
MATH 2130 Engineering Mathematical Analysis
MATH 2160 Numerical Analysis 1
MATH 3420 Numerical Analysis 2
MATH 4330/7330 Fundamentals of Approximation Theory
MATH 4440/7440 Numerical Analysis of Partial Differential Equations
MATH 4910/8410 Approximation Theory and Approximation Practice
MATH 8140 Advanced Numerical Analysis of Differential and Integral Equations

Links

https://home.cc.umanitoba.ca/~slevinrm/

https://github.com/MikaelSlevinsky

https://twitter.com/MikaelSlevinsky

B. Klippenstein and R. M. Slevinsky, Fast associated classical orthogonal polynomial transforms, J. Comp. Appl. Math., 403: 113831, 2022.
S. Olver, R. M. Slevinsky and A. Townsend, Fast algorithms using orthogonal polynomials, Acta Numerica, 29: 573–699, 2020.
J. L. Aurentz and R. M. Slevinsky, On symmetrizing the ultraspherical spectral method for self-adjoint problems, J. Comp. Phys., 410: 109383, 2020.
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.
R. M. Slevinsky, Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series, Appl. Comput. Harmon. Anal., 47: 585–606, 2019.
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.
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.
R. M. Slevinsky and S. Olver, A fast and well-conditioned spectral method for singular integral equations, J. Comp. Phys., 332: 290–315, 2017.
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.
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.
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.
R. M. Slevinsky and H. Safouhi, Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation, Numer. Algor., 66: 457–477, 2014.
P. Gaudreau, R. M. Slevinsky, and H. Safouhi, An asymptotic expansion for energy eigenvalues for anharmonic oscillators, Ann. Phys., 337: 261–277, 2013.
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.
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.
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.
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.
R. M. Slevinsky and H. Safouhi, New formulae for higher order derivatives and applications, J. Comp. Appl. Math., 233: 405–419, 2009.
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.
M. Slevinsky and H. Safouhi, Numerical treatment of a twisted tail using extrapolation methods, Numer. Algor., 48: 301–316, 2008.

B. Klippenstein and R. M. Slevinsky, Fast associated classical orthogonal polynomial transforms, J. Comp. Appl. Math., 403: 113831, 2022.
S. Olver, R. M. Slevinsky and A. Townsend, Fast algorithms using orthogonal polynomials, Acta Numerica, 29: 573–699, 2020.
J. L. Aurentz and R. M. Slevinsky, On symmetrizing the ultraspherical spectral method for self-adjoint problems, J. Comp. Phys., 410: 109383, 2020.
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.
R. M. Slevinsky, Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series, Appl. Comput. Harmon. Anal., 47: 585–606, 2019.
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.
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.
R. M. Slevinsky and S. Olver, A fast and well-conditioned spectral method for singular integral equations, J. Comp. Phys., 332: 290–315, 2017.
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.
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.
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.
R. M. Slevinsky and H. Safouhi, Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation, Numer. Algor., 66: 457–477, 2014.
P. Gaudreau, R. M. Slevinsky, and H. Safouhi, An asymptotic expansion for energy eigenvalues for anharmonic oscillators, Ann. Phys., 337: 261–277, 2013.
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.
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.
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.
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.
R. M. Slevinsky and H. Safouhi, New formulae for higher order derivatives and applications, J. Comp. Appl. Math., 233: 405–419, 2009.
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.
M. Slevinsky and H. Safouhi, Numerical treatment of a twisted tail using extrapolation methods, Numer. Algor., 48: 301–316, 2008.