4 papers
Nonlocal vector calculus on the sphere
Hadrien Montanelli, Richard Mikael Slevinsky, Qiang Du
We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar…
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…
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…