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...
متن کاملDerivation of the Trapezoidal Rule Error Estimate
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 ...
متن کاملNotes on the convergence of trapezoidal - rule quadrature
Numerical quadrature is another name for numerical integration, which refers to the approximation of an integral ́ f (x)dx of some function f (x) by a discrete summation ∑wi f (xi) over points xi with some weights wi. There are many methods of numerical quadrature corresponding to different choices of points xi and weights wi, from Euler integration to sophisticated methods such as Gaussian quad...
متن کاملA Simple Rule for Proteins to Follow
Proteins are the workhorses of cells, acting as enzymes, structural elements, and signal transducers. The tremendous variability in proteins’ chemical and physical properties is achieved through the manner in which they are made—by the mixing and matching of a set of basic building blocks known as amino acids. Each amino acid consists of a carbon atom attached to an amine group, a carboxyl grou...
متن کاملA Simple , Fast , and E ective Rule
We describe SLIPPER, a new rule learner that generates rulesets by repeatedly boosting a simple, greedy, rule-builder. Like the rulesets built by other rule learners , the ensemble of rules created by SLIPPER is compact and comprehensible. This is made possible by imposing appropriate constraints on the rule-builder, and by use of a recently-proposed generalization of Ad-aboost called conndence...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1967
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-67-99892-4