Accurate evaluation of polynomials in Legendre basis

DOI10.1155/2014/742538zbMath1442.65023OpenAlexW2099417434WikidataQ59052157 ScholiaQ59052157MaRDI QIDQ2336684

Hao Jiang, Li-Zhi Cheng, Pei-Bing Du

Publication date: 19 November 2019

Published in: Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/742538

Mathematics Subject Classification ID

Roundoff error (65G50) Computation of special functions and constants, construction of tables (65D20)

Related Items (3)

Accurate quotient-difference algorithm: error analysis, improvements and applications ⋮ Numerical validation of compensated algorithms with stochastic arithmetic ⋮ An accurate algorithm for evaluating rational functions

Uses Software

• mctoolbox
• LBNL
• XBLAS

Cites Work

• High-precision computation: mathematical physics and dynamics
• Accurate evaluation of a polynomial in Chebyshev form
• Accurate evaluation of a polynomial and its derivative in Bernstein form
• Algorithms for accurate, validated and fast polynomial evaluation
• Rounding error propagation in polynomial evaluation schemes
• Polynomial evaluation and associated polynomials
• A unified rounding error bound for polynomial evaluation
• Backward stability of Clenshaw's algorithm
• Accurate evaluation of the \(k\)-th derivative of a polynomial and its application
• A floating-point technique for extending the available precision
• A General Condition Number for Polynomials
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Product and Exponentiation
• Design, implementation and testing of extended and mixed precision BLAS
• Accurate Sum and Dot Product
• Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series
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