A comparison of some Taylor and Chebyshev series

Author:
R. E. Scraton

Journal:
Math. Comp. **50** (1988), 207-213

MSC:
Primary 41A50; Secondary 40A05, 41A58, 65B10

MathSciNet review:
917828

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Abstract: A function is approximated in the interval by (i) a Taylor series in *x*; (ii) a Taylor series in ; (iii) a Chebyshev series in *x*; and (iv) a Chebyshev series in . The convergence of all four series is discussed, and a method is given for finding the values of and which optimize convergence. Methods are also given for transforming one of the above series into another, some of which provide effective methods for acceleration of convergence. The application of the theory to even and odd functions is also discussed.

**[1]**R. E. Scraton,*A note on the summation of divergent power series*, Proc. Cambridge Philos. Soc.**66**(1969), 109–114. MR**0244667****[2]**R. E. Scraton,*A method for improving the convergence of Chebyshev series*, Comput. J.**13**(1970), 202–203. MR**0260144****[3]**F. Locher, "Accelerating the convergence of Chebyshev series,"*Computing*, v. 15, 1975, pp. 235-246.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1988-0917828-4

Article copyright:
© Copyright 1988
American Mathematical Society