Fast algorithms using orthogonal polynomials (Q5887824)

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scientific article; zbMATH DE number 7674566

Language	Label	Description	Also known as
English	Fast algorithms using orthogonal polynomials	scientific article; zbMATH DE number 7674566

Statements

scholarly article

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Fast algorithms using orthogonal polynomials (English)

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Richard Mikael Slevinsky

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publication date

14 April 2023

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describes a project that uses

Clenshaw-Curtis

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FastTransforms.jl

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SingularIntegralEquations

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FastGaussQuadrature

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Digital Library of Mathematical Functions

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MaRDI profile type

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full work available at URL

https://doi.org/10.1017/s0962492920000045

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A Fast Algorithm for the Evaluation of Legendre Expansions

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Spherical harmonics and approximations on the unit sphere. An introduction

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On symmetrizing the ultraspherical spectral method for self-adjoint problems

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Chopping a Chebyshev Series

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A Comparison of Three High-Precision Quadrature Schemes

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Focused tsunami waves

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New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials

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Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights

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$\mathcal{O}(1)$ Computation of Legendre Polynomials and Gauss--Legendre Nodes and Weights for Parallel Computing

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Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix

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Fast algorithms for Jacobi expansions via nonoscillatory phase functions

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Rank-one modification of the symmetric eigenproblem

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A divide-and-conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semiseparable matrices

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Generalized Jacobi functions and their applications to fractional differential equations

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An Algorithm for the Machine Calculation of Complex Fourier Series

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An efficient spectral method for ordinary differential equations with rational function coefficients

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Reduction of a band-symmetric generalized eigenvalue problem

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A Divide and Conquer method for the symmetric tridiagonal eigenproblem

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Approximation Theory and Harmonic Analysis on Spheres and Balls

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Abscissas and weights for Gaussian quadratures of high order

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Additional abscissas and weights for Gaussian quadratures of high order: Values for n=64, 80, and 96

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Efficient Spectral-Galerkin Algorithms for Direct Solution of Second-Order Equations Using Ultraspherical Polynomials

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Fast Discrete Polynomial Transforms with Applications to Data Analysis for Distance Transitive Graphs

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Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

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A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS

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Spectral methods on triangles and other domains

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Orthogonal Polynomials of Several Variables

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Fast Fourier Transforms for Nonequispaced Data

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From random matrices to stochastic operators

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The Classical Collocation Method for Singular Integral Equations

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A divide-and-conquer method for the tridiagonal generalized eigenvalue problem

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On Estimates for the Weights in Gaussian Quadrature in the Ultraspherical Case

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Inequalities for the Zeros of Ultraspherical Polynomials and Bessel Functions

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Fast Poisson solvers for spectral methods

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Computational Aspects of Three-Term Recurrence Relations

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Minimal Solutions of Three-Term Recurrence Relations and Orthogonal Polynomials

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On Generating Orthogonal Polynomials

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On mean convergence of extended Lagrange interpolation

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Computing the Hilbert transform of a Jacobi weight function

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Implementing Clenshaw-Curtis quadrature, I methodology and experience

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Asymptotic Approximations to the Nodes and Weights of Gauss–Hermite and Gauss–Laguerre Quadratures

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Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

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Noniterative Computation of Gauss--Jacobi Quadrature

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A Fast Algorithm for the Calculation of the Roots of Special Functions

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Calculation of Gauss Quadrature Rules

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Spectral Integration and Two-Point Boundary Value Problems

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Accelerating the Nonuniform Fast Fourier Transform

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A fast algorithm for particle simulations

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A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem

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A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem

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Vibrations of non-uniform rings studied by means of the differential quadrature method

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A Fast and Spectrally Convergent Algorithm for Rational-Order Fractional Integral and Differential Equations

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Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights

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A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula

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FFTs for the 2-sphere-improvements and variations

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Spectral methods with sparse matrices

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On the Fourier Extension of Nonperiodic Functions

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Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods

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An Algorithm for the Banded Symmetric Generalized Matrix

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Gegenbauer polynomials and semiseparable matrices

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Computing with Expansions in Gegenbauer Polynomials

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Quadrature by expansion: a new method for the evaluation of layer potentials

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Certain differential equations for Tchebycheff polynomials

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Universality of the Stochastic Airy Operator

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Fast spherical Fourier algorithms.

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Trigonometric Interpolation of Empirical and Analytical Functions

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A Fast Adaptive Numerical Method for Stiff Two-Point Boundary Value Problems

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On the construction of Gauss-Legendre quadrature rules

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Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle

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Galerkin orthogonal polynomials

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Table of the zeros of the Legendre polynomials of order 1-16 and the weight coefficients for Gauss’ mechanical quadrature formula

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Natural Orbitals in the Quantum Theory of Two-Electron Systems

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Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials

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An Accelerated Kernel-Independent Fast Multipole Method in One Dimension

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Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms

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A fast transform for spherical harmonics

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Computation of connection coefficients and measure modifications for orthogonal polynomials

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Numerical solution of second-order linear difference equations

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Computing the Hilbert transform and its inverse

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A general framework for solving Riemann-Hilbert problems numerically

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A Fast and Well-Conditioned Spectral Method

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Non-homogeneous wave equation on a cone

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Orthogonal structure on a wedge and on the boundary of a square

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Orthogonal polynomials in and on a quadratic surface of revolution

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A Sparse Spectral Method on Triangles

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Recurrence relations for a family of orthogonal polynomials on a triangle

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The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices

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On the computation of the Gauss-Legendre quadrature formula with a given precision

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Fast Summation at Nonequispaced Knots by NFFT

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Fast and stable algorithms for discrete spherical Fourier transforms

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The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

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Fast Algorithms for Spherical Harmonic Expansions

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Co-recursive orthogonal polynomials and fourth-order differential equation

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Fourth-order differential equations satisfied by the generalized co- recursive of all classical orthogonal polynomials. A study of their distribution of zeros

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A Nonuniform Fast Fourier Transform Based on Low Rank Approximation

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On a modification of the QD-algorithm with Graeffe-type convergence

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Tridiagonalization of a symmetric band matrix

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Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials

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Fast associated classical orthogonal polynomial transforms

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On the use of Hahn’s asymptotic formula and stabilized recurrence for a fast, simple and stable Chebyshev–Jacobi transform

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Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series

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A fast and well-conditioned spectral method for singular integral equations

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A spectral method for nonlocal diffusion operators on the sphere

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Sparse spectral and ‐finite element methods for partial differential equations on disk slices and trapeziums

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Fast construction of Fejér and Clenshaw-Curtis rules for general weight functions

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A fast spherical harmonics transform algorithm

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On Computing the Points and Weights for Gauss--Legendre Quadrature

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Pseudospectral Solution of the Two-Dimensional Navier--Stokes Equations in a Disk

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The automatic solution of partial differential equations using a global spectral method

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An Extension of Chebfun to Two Dimensions

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Fast computation of Gauss quadrature nodes and weights on the whole real line

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Fast polynomial transforms based on Toeplitz and Hankel matrices

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Is Gauss Quadrature Better than Clenshaw–Curtis?

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Riemann–Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions

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Fast algorithms for spherical harmonic expansions. II.

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Fast algorithms for spherical harmonic expansions. III

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Recurrence relations and fast algorithms

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Tensor calculus in polar coordinates using Jacobi polynomials

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Spectral integration of linear boundary value problems

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Superfast Divide-and-Conquer Method and Perturbation Analysis for Structured Eigenvalue Solutions

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Visual Complex Functions

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Computing with Functions in Spherical and Polar Geometries II. The Disk

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Approximation and orthogonality in Sobolev spaces on a triangle

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Accurate computation of weights in classical Gauss-Christoffel quadrature rules

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Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros

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Fractional Spectral Collocation Method

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A Chebyshev method for the solution of boundary value problems

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Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode

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Identifiers

10.1017/S0962492920000045

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5887824

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