The Exponentially Convergent Trapezoidal Rule
نویسندگان
چکیده
منابع مشابه
The Exponentially Convergent Trapezoidal Rule
It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special funct...
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and |g′′(x)| = M. We will show that |f(x)| ≤ g(x) on [0, 1]. The desired conclusion follows. Suppose however that this is false, that there is a number q ∈ [0, 1] for which f(q) > g(q). (The other case, f(q) < −g(q), is similar.) Our strategy will be to show that there are real numbers s and t with s < t such that f ′(s) > g′(s) and f ′(t) < g′(t). See figure. We will then apply the Mean Value ...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2014
ISSN: 0036-1445,1095-7200
DOI: 10.1137/130932132