Introduction to Scientific Computing and Data Analysis by Mark H. Holmes

Author:Mark H. Holmes
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

As a final note, the explanation for the error formula in Theorem 6.1 used the Taylor series in (6.4). Using the series in this way gives rise to what is known as the asymptotic form of the error, and this is explained in Appendix C. A formal proof of the theorem can be obtained using the remainder form of the Taylor series and knowing certain inequalities involving integrals. This approach, using the series rather than the remainder version of a Taylor series to derive the formula for the error, is often used in this chapter. In each case, for those so inclined, a more rigorous proof can be obtained using similar modifications to the argument given.

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