On the numerical evaluation of linear recurrences
type: Item
instance of: scholarly article
title: On the numerical evaluation of linear recurrences
zbMATH Open document ID: 1015.65072
DOI: 10.1016/S0377-0427(02)00565-4
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 2003-03-12T00:00:00Z
review text: Investigation of the rounding errors for the evaluation of \(n\)-term linear recurrences of order \(m+1\). For several examples the new result is compared with the exact error and an old estimate. Then the parallel evaluation of the last term of a recurrence is discussed with an algorithm based on Stone's algorithm. Speedup examples on a T3E are presented for different values of \(m,n\) and number of processors up to 512.
Mathematics Subject Classification ID: 65Q05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 1880337
zbMATH Keywords: linear recurrence relations
zbMATH Keywords: rounding errors
zbMATH Keywords: parallel algorithms
zbMATH Keywords: Stone's algorithm
describes a project that uses: mctoolbox
MaRDI profile type: Publication
cites work: On Orthogonal Polynomials of Sobolev Type: Algebraic Properties and Zeros
cites work: Q4052481
cites work: Associated Laguerre and Hermite polynomials
cites work: Parallel Algorithms to Evaluate Orthogonal Polynomial Series
cites work: Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series
cites work: Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. I: Algorithms
cites work: A Parallel Algorithm to Evaluate Chebyshev Series on a Message Passing Environment
cites work: Time and Parallel Processor Bounds for Linear Recurrence Systems
cites work: Q5849046
cites work: On Recurrence Relations for Sobolev Orthogonal Polynomials
cites work: Fourth-order difference equation for the associated classical discrete orthogonal polynomials
cites work: Q4864704
cites work: The Complexity of Parallel Evaluation of Linear Recurrences
cites work: Results on the associated Jacobi and Gegenbauer polynomials
cites work: Solutions of linear difference equations with variable coefficients
cites work: Rounding error propagation in polynomial evaluation schemes
cites work: Q4370389
cites work: Fourth-order difference equation for the first associated of classical discrete orthogonal polynomials
cites work: Recurrence relations for connection coefficients between two families of orthogonal polynomials
cites work: Parallel Tridiagonal Equation Solvers
cites work: Connection Coefficients of Orthogonal Polynomials
cites work: Condition Numbers of Random Triangular Matrices
cites work: Resurrecting the asymptotics of linear recurrences
description: scientific article; zbMATH DE number 1880337