Search Results - "Olver, Sheehan"

Spectra of Jacobi Operators via Connection Coefficient Matrices by Webb, Marcus, Olver, Sheehan

“…We address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a…”
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A Fast and Well-Conditioned Spectral Method by Olver, Sheehan, Townsend, Alex

“…A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients and general boundary conditions…”
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Sparse spectral and p‐finite element methods for partial differential equations on disk slices and trapeziums by Snowball, Ben, Olver, Sheehan

“…Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on…”
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Computing the Hilbert transform and its inverse by OLVER, SHEEHAN

“…We construct a new method for approximating Hilbert transforms and their inverse throughout the complex plane. Both problems can be formulated as…”
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Fast polynomial transforms based on Toeplitz and Hankel matrices by TOWNSEND, ALEX, WEBB, MARCUS, OLVER, SHEEHAN

“…Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard…”
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Orthogonal Polynomials on Planar Cubic Curves by Fasondini, Marco, Olver, Sheehan, Xu, Yuan

“…Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic…”
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Orthogonal Structure on a Wedge and on the Boundary of a Square by Olver, Sheehan, Xu, Yuan

“…Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly…”
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Non-homogeneous wave equation on a cone by Olver, Sheehan, Xu, Yuan

“…The wave equation in the cone is shown to have a unique solution if u and its partial derivatives in x are in on the cone, and the solution can be explicit…”
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Orthogonal polynomials on a class of planar algebraic curves by Fasondini, Marco, Olver, Sheehan, Xu, Yuan

“…We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form ym=ϕ(x)$y^{m} = \phi (x)$ in R2${\mathbb {R}}^2$ where m=1,2$m = 1, 2$ and…”
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A sparse spectral method for fractional differential equations in one-spatial dimension by Papadopoulos, Ioannis P. A., Olver, Sheehan

“…We develop a sparse spectral method for a class of fractional differential equations, posed on R , in one dimension. These equations may include…”
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Moment-free numerical integration of highly oscillatory functions by OLVER, Sheehan

“…The aim of this paper is to derive new methods for numerically approximating the integral of a highly oscillatory function. We begin with a review of the…”
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Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension by Gutleb, Timon S., Carrillo, José A., Olver, Sheehan

“…We present a numerical approach for computing attractive-repulsive power law equilibrium measures in arbitrary dimension. We prove new recurrence relationships…”
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Numerical methods for the computation of the confluent and Gauss hypergeometric functions by Pearson, John W., Olver, Sheehan, Porter, Mason A.

“…The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available…”
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On the convergence rate of a modified Fourier series by Olver, Sheehan

“…The rate of convergence for an orthogonal series that is a minor modification of the Fourier series is proved. This series converges pointwise at a faster rate…”
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Universality in numerical computations with random data by Deift, Percy A., Menon, Govind, Olver, Sheehan, Trogdon, Thomas

“…Significance Universal fluctuations are shown to exist when well-known and widely used numerical algorithms are applied with random data. Similar universal…”
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The automatic solution of partial differential equations using a global spectral method by Townsend, Alex, Olver, Sheehan

“…A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular…”
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A general framework for solving Riemann–Hilbert problems numerically by Olver, Sheehan

“…A new, numerical framework for the approximation of solutions to matrix-valued Riemann–Hilbert problems is developed, based on a recent method for the…”
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A Practical Framework for Infinite-Dimensional Linear Algebra by Olver, Sheehan, Townsend, Alex

“…We describe a framework for solving a broad class of infinite-dimensional linear equations, consisting of almost banded operators, which can be used to…”
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Orthogonal structure on a quadratic curve by Olver, Sheehan, Xu, Yuan

“…Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For…”
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A fast and well-conditioned spectral method for singular integral equations by Slevinsky, Richard Mikael, Olver, Sheehan

“…We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials…”
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