The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function
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- Math. Comp. 18 (1964), 274-284 Request permission
References
- C. W. Clenshaw and A. R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960), 197–205. MR 117885, DOI 10.1007/BF01386223
- C. W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proc. Cambridge Philos. Soc. 53 (1957), 134–149. MR 82196, DOI 10.1017/s0305004100032072
- L. Fox, Chebyshev methods for ordinary differential equations, Comput. J. 4 (1961/62), 318–331. MR 136521, DOI 10.1093/comjnl/4.4.318
- C. W. Clenshaw and H. J. Norton, The solution of nonlinear ordinary differential equations in Chebyshev series, Comput. J. 6 (1963/64), 88–92. MR 155433, DOI 10.1093/comjnl/6.1.88
- David Elliott, The numerical solution of integral equations using Chebyshev polynomials, J. Austral. Math. Soc. 1 (1959/1960), 344–356. MR 0128087
- David Elliott, Chebyshev series method for the numerical solution of Fredholm integral equations, Comput. J. 6 (1963/64), 102–111. MR 155452, DOI 10.1093/comjnl/6.1.102
- David Elliott, A method for the numerical integration of the one-dimensional heat equation using Chebyshev series, Proc. Cambridge Philos. Soc. 57 (1961), 823–832. MR 130126 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, v. 1. McGraw-Hill, New York, 1953.
- E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Chelsea Publishing Co., New York, 1955. MR 0064922 J. Wimp, “Polynomial approximations to integral transforms,” Math. Comp., v. 15, 1961, p. 174. G. Szegö, “Orthogonal polynomials,” Amer. Math. Soc. Colloquium Publication v. 23, 1939.
- W. Barrett, Convergence properties of Gaussian quadrature formulae, Comput. J. 3 (1960/61), 272–277. MR 128073, DOI 10.1093/comjnl/3.4.272
Additional Information
- © Copyright 1964 American Mathematical Society
- Journal: Math. Comp. 18 (1964), 274-284
- MSC: Primary 65.25
- DOI: https://doi.org/10.1090/S0025-5718-1964-0166903-7
- MathSciNet review: 0166903