Truncation errors in two Chebyshev series approximations

Author:
David Elliott

Journal:
Math. Comp. **19** (1965), 234-248

MSC:
Primary 65.20

DOI:
https://doi.org/10.1090/S0025-5718-1965-0181084-2

MathSciNet review:
0181084

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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 & A. R. Curtis, "A method for numerical integration on an automatic computer,"*Numer. Math.*, v. 2, 1960, pp. 197-205. 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. 274-284. MR**0166903 (29:4176)****[6]**J. Todd (Ed.),*Survey of Numerical Analysis*, McGraw-Hill, New York, 1962, pp. 1-159. 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. 123-199.**[8]**D. Elliott & G. Szekeres, "Some estimates of the coefficients in the Chebyshev series expansion of a function,"*Math. Comp.*, v. 19, 1965, pp. 25-32. MR**0172447 (30:2666)****[9]**N. G. de Bruijn,*Asymptotic Methods in Analysis*, Bibliotheca Mathematica, Vol. 4, North-Holland, 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 non-linear ordinary differential equations in Chebyshev series,"*Comput. J.*, v. 6, 1963/64, pp. 88-92. 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. 102-111. MR**0155452 (27:5386)**

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DOI:
https://doi.org/10.1090/S0025-5718-1965-0181084-2

Article copyright:
© Copyright 1965
American Mathematical Society