Truncation errors in two Chebyshev series approximations
Author:
David Elliott
Journal:
Math. Comp. 19 (1965), 234248
MSC:
Primary 65.20
MathSciNet review:
0181084
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [1]
Tables of Chebyshev Polynomials, National Bureau of Standards Applied Mathematics Series, No. 9, U.S. Government Printing Office, Washington, 1952; introduction by C. Lanczos.
 [2]
C.
W. Clenshaw and A.
R. Curtis, A method for numerical integration on an automatic
computer, Numer. Math. 2 (1960), 197–205. MR 0117885
(22 #8659)
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W. Clenshaw, Chebyshev series for mathematical functions,
National Physical Laboratory Mathematical Tables, Vol. 5. Department of
Scientific and Industrial Research, Her Majesty’s Stationery Office,
London, 1962. MR
0142793 (26 #362)
 [4]
C.
W. Clenshaw, A comparison of “best” polynomial
approximations with truncated Chebyshev series expansions, J. Soc.
Indust. Appl. Math. Ser. B Numer. Anal. 1 (1964),
26–37. MR
0179530 (31 #3778)
 [5]
David
Elliott, The evaluation and estimation of the
coefficients in the Chebyshev series expansion of a function, Math. Comp. 18 (1964), 274–284. MR 0166903
(29 #4176), http://dx.doi.org/10.1090/S00255718196401669037
 [6]
Survey of numerical analysis, McGrawHill Book Co., Inc., New
YorkTorontoLondon, 1962. MR 0135221
(24 #B1271)
 [7]
C. Lanczos, "Trigonometric interpolation of empirical and analytical functions," J. Math. Phys., v. 17, 1938, pp. 123199.
 [8]
David
Elliott and George
Szekeres, Some estimates of the coefficients in
the Chebyshev series expansion of a function, Math. Comp. 19 (1965), 25–32. MR 0172447
(30 #2666), http://dx.doi.org/10.1090/S0025571819650172447X
 [9]
N.
G. de Bruijn, Asymptotic methods in analysis, Bibliotheca
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 [10]
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equations in Chebyshev series, Comput. J. 6
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(27 #5367)
 [11]
David
Elliott, Chebyshev series method for the numerical solution of
Fredholm integral equations, Comput. J. 6
(1963/1964), 102–111. MR 0155452
(27 #5386)
 [1]
 Tables of Chebyshev Polynomials, National Bureau of Standards Applied Mathematics Series, No. 9, U.S. Government Printing Office, Washington, 1952; introduction by C. Lanczos.
 [2]
 C. W. Clenshaw & A. R. Curtis, "A method for numerical integration on an automatic computer," Numer. Math., v. 2, 1960, pp. 197205. MR 22 #8659. MR 0117885 (22:8659)
 [3]
 C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Laboratories Mathematical Tables, Vol. 5, Department of Scientific and Industrial Research, Her Majesty's Stationery Office, London, 1962. MR 26 #362. MR 0142793 (26:362)
 [4]
 C. W. Clenshaw, "A comparison of "best" polynomial approximations with truncated Chebyshev series expansion," Contribution to 1963 Conference on Approximation, at Gatlinburg. (To appear in J. SIAM. Control Ser. A.) MR 0179530 (31:3778)
 [5]
 D. Elliott, "The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function," Math. Comp., v. 18, 1964, pp. 274284. MR 0166903 (29:4176)
 [6]
 J. Todd (Ed.), Survey of Numerical Analysis, McGrawHill, New York, 1962, pp. 1159. MR 24 #B1746; MR 25 #1630; MR 25 #1631. MR 0135221 (24:B1271)
 [7]
 C. Lanczos, "Trigonometric interpolation of empirical and analytical functions," J. Math. Phys., v. 17, 1938, pp. 123199.
 [8]
 D. Elliott & G. Szekeres, "Some estimates of the coefficients in the Chebyshev series expansion of a function," Math. Comp., v. 19, 1965, pp. 2532. MR 0172447 (30:2666)
 [9]
 N. G. de Bruijn, Asymptotic Methods in Analysis, Bibliotheca Mathematica, Vol. 4, NorthHolland, Amsterdam, Noordhoff, Groningen and Interscience, New York, 1958. MR 20 #6003. MR 0099564 (20:6003)
 [10]
 C. W. Clenshaw & H. J. Norton, "The solution of nonlinear ordinary differential equations in Chebyshev series," Comput. J., v. 6, 1963/64, pp. 8892. MR 27 #5367. MR 0155433 (27:5367)
 [11]
 D. Elliott, "A Chebyshev series method for the numerical solution of Fredholm integral equations," Comput. J., v. 6, 1963, pp. 102111. MR 0155452 (27:5386)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196501810842
PII:
S 00255718(1965)01810842
Article copyright:
© Copyright 1965
American Mathematical Society
