13 citations · 28 across the 14 of their papers we have counts for
18 papers · 1 filter
Fast measure modification of orthogonal polynomials via matrices with displacement structure
Karim Gumerov, Samantha Rigg, Richard Mikael Slevinsky
It is well known that matrices with low Hessenberg-structured displacement rank enjoy fast algorithms for certain matrix factorizations. We show how principal finite se…
Building hierarchies of semiclassical Jacobi polynomials for spectral methods in annuli
Ioannis P. A. Papadopoulos, Timon S. Gutleb, Richard M. Slevinsky +1
We discuss computing with hierarchies of families of (potentially weighted) semiclassical Jacobi polynomials which arise in the construction of multivariate orthogonal polynomials.…
Lifting Sylvester equations: singular value decay for non-normal coefficients
Raphaël Clouâtre, Brock Klippenstein, Richard Mikaël Slevinsky
We aim to find conditions on two Hilbert space operators and under which the expression having low rank forces the operator itself to admit a good low rank appr…
Fast and stable rational approximation of generalized hypergeometric functions
Richard Mikael Slevinsky
Rational approximations of generalized hypergeometric functions of type are constructed by the Drummond and factorial Levin-type sequence transformations. We de…
Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations
Timon S. Gutleb, Sheehan Olver, Richard Mikael Slevinsky
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified m…
A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions
Richard M. Slevinsky, Hassan Safouhi
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the transformation and…
Fast associated classical orthogonal polynomial transforms
Brock Klippenstein, Richard Mikael Slevinsky
We discuss a fast approximate solution to the associated classical -- classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynom…
On symmetrizing the ultraspherical spectral method for self-adjoint problems
Jared Lee Aurentz, Richard Mikael Slevinsky
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is present…
Fast and accurate algorithms for the computation of spherically symmetric nonlocal diffusion operators on lattices
Yu Li, Richard Mikael Slevinsky
We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels wi…
A rapid and well-conditioned algorithm for the Helmholtz--Hodge decomposition of vector fields on the sphere
Julien Molina, Richard Mikael Slevinsky
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with…
A spectral method for nonlocal diffusion operators on the sphere
Richard Mikael Slevinsky, Hadrien Montanelli, Qiang Du
We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlo…
Conquering the pre-computation in two-dimensional harmonic polynomial transforms
Richard Mikael Slevinsky
We describe a skeletonization of the spherical harmonic connection problem that reduces the storage and pre-computation to superoptimal complexities at the cost of increasing the e…
Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series
Richard Mikael Slevinsky
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, e…
On the use of Hahn's asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev--Jacobi transform
Richard Mikael Slevinsky
We describe a fast, simple, and stable transform of Chebyshev expansion coefficients to Jacobi expansion coefficients and its inverse based on the numerical evaluation of Jacobi ex…
A fast and well-conditioned spectral method for singular integral equations
Richard Mikael Slevinsky, Sheehan Olver
We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the eq…
Computing Energy Eigenvalues of Anharmonic Oscillators using the Double Exponential Sinc collocation Method
Philippe Gaudreau, Richard Slevinsky, Hassan Safouhi
A quantum anharmonic oscillator is defined by the Hamiltonian , where the potential is given by $V(x) = \sum_{i=1}^{m} c_{i} x^…
The Double Exponential Sinc Collocation Method for Singular Sturm-Liouville Problems
Philippe Gaudreau, Richard Slevinsky, Hassan Safouhi
Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate me…
On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods
Richard Mikael Slevinsky, Sheehan Olver
We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the…