메뉴 건너뛰기




Volumn 55, Issue 9, 2012, Pages 1749-1760

Chebfun and numerical quadrature

Author keywords

barycentric interpolation formula; Chebfun; Clenshaw Curtis quadrature; fractional calculus; Gauss quadrature; Riemann Liouville integral

Indexed keywords


EID: 84865553498     PISSN: 16747283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-012-4474-z     Document Type: Article
Times cited : (26)

References (26)
  • 2
    • 4944240756 scopus 로고    scopus 로고
    • Barycentric Lagrange interpolation
    • Berrut J P, Trefethen L N. Barycentric Lagrange interpolation. SIAM Rev, 2004, 46: 501-517.
    • (2004) SIAM Rev , vol.46 , pp. 501-517
    • Berrut, J.P.1    Trefethen, L.N.2
  • 3
    • 0000624238 scopus 로고
    • A method for numerical integration on an automatic computer
    • Clenshaw C W, Curtis A R. A method for numerical integration on an automatic computer. Numer Math, 1960, 2: 197-205.
    • (1960) Numer Math , vol.2 , pp. 197-205
    • Clenshaw, C.W.1    Curtis, A.R.2
  • 4
    • 4043089116 scopus 로고    scopus 로고
    • Doubly adaptive quadrature routines based on Newton-Cotes rules
    • Espelid T O. Doubly adaptive quadrature routines based on Newton-Cotes rules. BIT Numer Math, 2003, 43: 319-337.
    • (2003) BIT Numer Math , vol.43 , pp. 319-337
    • Espelid, T.O.1
  • 5
    • 84865541521 scopus 로고    scopus 로고
    • Extended doubly adaptive quadrature routines
    • Department of Informatics, University of Bergen
    • Espelid T O. Extended doubly adaptive quadrature routines. Tech Rep 266. Department of Informatics, University of Bergen.
    • Tech Rep 266
    • Espelid, T.O.1
  • 6
    • 84976715209 scopus 로고
    • Implementing Clenshaw-Curtis quadrature I and II
    • Gentleman W M. Implementing Clenshaw-Curtis quadrature I and II. J ACM, 1972, 15: 337-346.
    • (1972) J ACM , vol.15 , pp. 337-346
    • Gentleman, W.M.1
  • 7
    • 40249111875 scopus 로고    scopus 로고
    • A fast algorithm for the calculation of the roots of special functions
    • Glaser A, Liu X, Rokhlin V. A fast algorithm for the calculation of the roots of special functions. SIAM J Sci Comp, 2007, 29: 1420-1438.
    • (2007) SIAM J Sci Comp , vol.29 , pp. 1420-1438
    • Glaser, A.1    Liu, X.2    Rokhlin, V.3
  • 8
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • Golub G H, Welsch J H. Calculation of Gauss quadrature rules. Math Comp, 1969, 23: 221-230.
    • (1969) Math Comp , vol.23 , pp. 221-230
    • Golub, G.H.1    Welsch, J.H.2
  • 9
    • 77957578733 scopus 로고    scopus 로고
    • Increasing the reliability of adaptive quadrature using explicit interpolants
    • Gonnet P. Increasing the reliability of adaptive quadrature using explicit interpolants. ACM Trans Math Softw, 2010, 37: 26: 2-26: 32.
    • (2010) ACM Trans Math Softw , vol.37 , pp. 2-32
    • Gonnet, P.1
  • 11
    • 84865574226 scopus 로고    scopus 로고
    • Fast and accurate computation of Gauss-Jacobi nodes and weights
    • Hale N, Townsend A. Fast and accurate computation of Gauss-Jacobi nodes and weights. In preparation, 2012.
    • (2012) Preparation
    • Hale, N.1    Townsend, A.2
  • 12
    • 7444229866 scopus 로고    scopus 로고
    • he numerical stability of barycentric Lagrange interpolation
    • Higham N J. The numerical stability of barycentric Lagrange interpolation. IMA J Numer Anal, 2004, 2: 547-556.
    • (2004) IMA J Numer Anal , vol.2 , pp. 547-556
    • Higham, N.J.T.1
  • 13
    • 84865536770 scopus 로고    scopus 로고
    • Octave software
    • Octave software. http://www. octave. org/.
  • 14
    • 0040800431 scopus 로고
    • Error estimation in the Clenshaw-Curtis quadrature formula
    • O'Hara H, Smith F J. Error estimation in the Clenshaw-Curtis quadrature formula. Comput J, 1968, 11: 213-219.
    • (1968) Comput J , vol.11 , pp. 213-219
    • O'Hara, H.1    Smith, F.J.2
  • 17
    • 0001369024 scopus 로고
    • n,ν = cos(νπ/n), ν = 0(1)n; some unnoted advantages
    • n,ν = cos(νπ/n), ν = 0(1)n; some unnoted advantages. Computer J, 1972, 15: 156-159.
    • (1972) Computer J , vol.15 , pp. 156-159
    • Salzer, H.E.1
  • 19
    • 0004073954 scopus 로고
    • Providence, RI: Amer Math Soc
    • Szego{double acute} G. Orthogonal Polynomials. Providence, RI: Amer Math Soc, 1939.
    • (1939) Orthogonal Polynomials
    • Szego, G.1
  • 20
    • 40749154941 scopus 로고    scopus 로고
    • Is Gauss quadrature better than Clenshaw-Curtis
    • Trefethen L N. Is Gauss quadrature better than Clenshaw-Curtis. SIAM Rev, 2008, 50: 67-87.
    • (2008) SIAM Rev , vol.50 , pp. 67-87
    • Trefethen, L.N.1
  • 21
    • 84865537769 scopus 로고    scopus 로고
    • Six myths of polynomial interpolation and quadrature
    • Trefethen L N. Six myths of polynomial interpolation and quadrature. Math Today, 2011, 47: 184-188.
    • (2011) Math Today , vol.47 , pp. 184-188
    • Trefethen, L.N.1
  • 24
    • 33645037515 scopus 로고    scopus 로고
    • Fast construction of the Fejér and Clenshaw-Curtis quadrature rules
    • Waldvogel J. Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT Numer Math, 2006, 46: 195-202.
    • (2006) BIT Numer Math , vol.46 , pp. 195-202
    • Waldvogel, J.1
  • 25
    • 84858980863 scopus 로고    scopus 로고
    • On the convergence rates of Legendre approximation
    • Wang H, Xiang S. On the convergence rates of Legendre approximation. Math Comp, 2012, 81: 861-877.
    • (2012) Math Comp , vol.81 , pp. 861-877
    • Wang, H.1    Xiang, S.2
  • 26
    • 0347844212 scopus 로고
    • On mechanical quadratures formulae involving the classical orthogonal polynomials
    • Winston C. On mechanical quadratures formulae involving the classical orthogonal polynomials. Ann Math, 1934, 35: 658-677.
    • (1934) Ann Math , vol.35 , pp. 658-677
    • Winston, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.