Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights
暂无分享,去创建一个
[1] Nicholas Hale,et al. Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights , 2013, SIAM J. Sci. Comput..
[2] Yunshyong Chow,et al. A Bernstein-type inequality for the Jacobi polynomial , 1994 .
[3] Knut Petras,et al. On the computation of the Gauss-Legendre quadrature formula with a given precision , 1999 .
[4] L. Trefethen. Six myths of polynomial interpolation and quadrature , 2011 .
[5] Ignace Bogaert,et al. Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights , 2014, SIAM J. Sci. Comput..
[6] Fredrik Johansson,et al. Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic , 2016, IEEE Transactions on Computers.
[7] K. Petras. Self-validating integration and approximation of piecewise analytic functions , 2002 .
[8] Ronald F. Boisvert,et al. NIST Handbook of Mathematical Functions , 2010 .
[9] Fredrik Johansson. Efficient Implementation of Elementary Functions in the Medium-Precision Range , 2015, 2015 IEEE 22nd Symposium on Computer Arithmetic.
[10] Fredrik Johansson,et al. Computing Hypergeometric Functions Rigorously , 2016, ACM Trans. Math. Softw..
[11] Jonathan M. Borwein,et al. High-precision numerical integration: Progress and challenges , 2008, J. Symb. Comput..
[12] J. Borwein,et al. Integrals of the Ising Class , 2006 .
[13] David Broadhurst,et al. Feynman integrals, L-series and Kloosterman moments , 2016, 1604.03057.
[14] Fredrik Johansson,et al. Evaluating parametric holonomic sequences using rectangular splitting , 2013, ISSAC.
[15] Gene H. Golub,et al. Calculation of Gauss quadrature rules , 1967, Milestones in Matrix Computation.
[16] Masatake Mori,et al. Double Exponential Formulas for Numerical Integration , 1973 .
[17] Laurent Fousse,et al. Accurate Multiple-Precision Gauss-Legendre Quadrature , 2007, 18th IEEE Symposium on Computer Arithmetic (ARITH '07).
[18] Lloyd N. Trefethen,et al. Is Gauss Quadrature Better than Clenshaw-Curtis? , 2008, SIAM Rev..
[19] David M. Smith,et al. Efficient multiple-precision evaluation of elementary functions , 1989 .
[20] Ramon E. Moore. Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.
[21] D. V. Chudnovsky,et al. Computer Algebra in the Service of Mathematical Physics and Number Theory , 2020, Computers in Mathematics.
[22] I. BOGAERT,et al. O(1) Computation of Legendre Polynomials and Gauss-Legendre Nodes and Weights for Parallel Computing , 2012, SIAM J. Sci. Comput..
[23] H. Woźniakowski,et al. Is Gauss quadrature optimal for analytic functions? , 1985 .
[24] Richard P. Brent,et al. Asymptotic approximation of central binomial coefficients with rigorous error bounds , 2016, Open Journal of Mathematical Sciences.
[25] F. Olver. Asymptotics and Special Functions , 1974 .
[26] Jet Wimp,et al. Computation with recurrence relations , 1986 .
[27] Richard P. Brent,et al. Modern Computer Arithmetic , 2010 .
[28] Fredrik Johansson. Computing Stieltjes constants using complex integration , 2019, Math. Comput..
[29] Aaas News,et al. Book Reviews , 1893, Buffalo Medical and Surgical Journal.
[30] Xiaoye S. Li,et al. ARPREC: An arbitrary precision computation package , 2002 .
[31] Michael Sagraloff,et al. Fast Approximate Polynomial Multipoint Evaluation and Applications , 2013, ArXiv.