메뉴 건너뛰기




Volumn 121, Issue 1, 2000, Pages 113-124

Computing integral transforms and solving integral equations using Chebyshev polynomial approximations

Author keywords

[No Author keywords available]

Indexed keywords

CHEBYSHEV APPROXIMATION; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; MATHEMATICAL TRANSFORMATIONS; POLYNOMIALS; THEOREM PROVING;

EID: 0034274840     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00349-6     Document Type: Article
Times cited : (53)

References (26)
  • 1
    • 84968505704 scopus 로고
    • A note on the summation of Chebyshev series
    • C.W. Clenshaw A note on the summation of Chebyshev series Math. Tab. Wash 9 1955 118 120
    • (1955) Math. Tab. Wash , vol.9 , pp. 118-120
    • Clenshaw, C.W.1
  • 2
    • 2142648377 scopus 로고
    • Curve fitting with a digital computer
    • C.W. Clenshaw Curve fitting with a digital computer Comput. J. 2 1960 170 173
    • (1960) Comput. J. , vol.2 , pp. 170-173
    • Clenshaw, C.W.1
  • 3
    • 85120136718 scopus 로고
    • C.W. Clenshaw Chebyshev Series for Mathematical Functions Math. Tab. Nat. Phip. Lab. Vol. 5 1962 H.M. Stationery Office London
    • (1962)
    • Clenshaw, C.W.1
  • 4
    • 0000624238 scopus 로고
    • A method for numerical integration on an automatic computer
    • C.W. Clenshaw A.R. Curtis A method for numerical integration on an automatic computer Numer. Math. 2 1960 197 205
    • (1960) Numer. Math. , vol.2 , pp. 197-205
    • Clenshaw, C.W.1    Curtis, A.R.2
  • 5
    • 0042140532 scopus 로고
    • A Chebyshev series method for the numerical solution of Fredholm integral equations
    • D. Elliott A Chebyshev series method for the numerical solution of Fredholm integral equations Comput. J. 6 1961 102 111
    • (1961) Comput. J. , vol.6 , pp. 102-111
    • Elliott, D.1
  • 6
    • 85120095207 scopus 로고
    • L. Fox I.B. Parker Chebyshev Polynomials in Numerical Analysis 1968 Oxford University Press London
    • (1968)
    • Fox, L.1    Parker, I.B.2
  • 7
    • 0001054517 scopus 로고
    • On the construction of Gaussian rules from modified moments
    • W. Gautschi On the construction of Gaussian rules from modified moments Math. Comput. 24 1970 245 260
    • (1970) Math. Comput. , vol.24 , pp. 245-260
    • Gautschi, W.1
  • 8
    • 84976783239 scopus 로고
    • Algorithm 424, Clenshaw–Curtis quadrature
    • W.M. Gentleman Algorithm 424, Clenshaw–Curtis quadrature Comm. ACM 15 1972 353 355
    • (1972) Comm. ACM , vol.15 , pp. 353-355
    • Gentleman, W.M.1
  • 9
    • 85162699057 scopus 로고
    • Trigonometric interpolation of empirical and analytic functions
    • C. Lanczos Trigonometric interpolation of empirical and analytic functions J. Math. Phys. 17 1938 123 199
    • (1938) J. Math. Phys. , vol.17 , pp. 123-199
    • Lanczos, C.1
  • 10
    • 85120133422 scopus 로고
    • C. Lanczos Tables of Chebyshev Polynomials Applicable Mathematics Series US Bureau Standards Vol. 9 1952 Government Printing Office Washington
    • (1952)
    • Lanczos, C.1
  • 11
    • 85120135714 scopus 로고
    • C. Lanczos Applied Analysis 1957 Prentice-Hall New York
    • (1957)
    • Lanczos, C.1
  • 12
    • 85120106204 scopus 로고
    • Y.L. Luke Integrals of Bessel functions 1962 McGraw-Hill Book Co New York
    • (1962)
    • Luke, Y.L.1
  • 13
    • 85120138089 scopus 로고
    • Y.L. Luke The Special Functions and their Approximations, Vols. 1 & 2 1969 Academic Press New York
    • (1969)
    • Luke, Y.L.1
  • 14
    • 85120128949 scopus 로고
    • Y.L. Luke Mathematical Functions and their Approximations 1975 Academic Press New York
    • (1975)
    • Luke, Y.L.1
  • 15
    • 85120120904 scopus 로고
    • Y.L. Luke Algorithms for the Computation of Mathematical Functions 1977 Academic Press New York
    • (1977)
    • Luke, Y.L.1
  • 16
    • 0040591543 scopus 로고
    • The numerical solution of linear recurrence relations
    • J. Oliver The numerical solution of linear recurrence relations Numer. Math. 11 1968 349 360
    • (1968) Numer. Math. , vol.11 , pp. 349-360
    • Oliver, J.1
  • 17
    • 77958410085 scopus 로고
    • A new numerical method for the inversion of the Laplace transform
    • R. Piessens A new numerical method for the inversion of the Laplace transform J. Inst. Math. Appl. 10 1972 185 192
    • (1972) J. Inst. Math. Appl. , vol.10 , pp. 185-192
    • Piessens, R.1
  • 18
    • 85120138305 scopus 로고
    • Modified Chenshaw–Curtis integration and applications to numerical computation of integral transforms
    • R. Piessens Modified Chenshaw–Curtis integration and applications to numerical computation of integral transforms P. Keast G. Fairweather Numerical Integrations: Recent Developments, Software and Applications 1987 Reidel Dordrecht
    • (1987)
    • Piessens, R.1
  • 19
    • 0001288628 scopus 로고
    • Numerical solution of integral equations of mathematical physics, using Chebyshev polynomials
    • R. Piessens M. Branders Numerical solution of integral equations of mathematical physics, using Chebyshev polynomials J. Comput. Phys. 21 1976 178 196
    • (1976) J. Comput. Phys. , vol.21 , pp. 178-196
    • Piessens, R.1    Branders, M.2
  • 20
    • 0021168319 scopus 로고
    • Computation of Fourier transform integrals using Chebyshev series expansions
    • R. Piessens M. Branders Computation of Fourier transform integrals using Chebyshev series expansions Computing 32 1984 177 186
    • (1984) Computing , vol.32 , pp. 177-186
    • Piessens, R.1    Branders, M.2
  • 23
    • 34250434098 scopus 로고
    • Numerical solution of the Abel integral equation
    • R. Piessens P. Verbaeten Numerical solution of the Abel integral equation BIT 13 1973 451 457
    • (1973) BIT , vol.13 , pp. 451-457
    • Piessens, R.1    Verbaeten, P.2
  • 24
    • 85120107766 scopus 로고
    • E.D. Rainville Special Functions 1960 Macmillan New York
    • (1960)
    • Rainville, E.D.1
  • 25
    • 85120132381 scopus 로고
    • T. Rivlin Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory 1990 Wiley New York
    • (1990)
    • Rivlin, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.