منابع مشابه
A Sequence of Polynomials for Approximating Arctangent
k=0 (−1)k 2k + 1 x } , the sequence of Taylor polynomials centered at 0 that converges to arctanx on [−1, 1]. Like the Taylor polynomials for several other classical functions, e.g., cosx, sinx, and ex, this sequence of polynomials is very easy to describe and work with; but unlike those Taylor sequences with factorials in the denominators of their coefficients, it does not converge rapidly for...
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Matchings in graphs correspond to independent sets in the corresponding line graphs. Line graphs are an important subclass of claw-free graphs. Hence studying independence polynomials of claw-free graphs is a natural extension of studying matching polynomials of graphs. We extend a result of Bayati et.al. showing a fully polynomial time approximation scheme (FPTAS) for computing the independenc...
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XS f dμ. It is natural to ask if the same is true for any linear functional L : R[X ] → R which is non-negative on MS. This is the Moment Problem for the quadratic module MS. The most interesting case seems to be when S is finite. A sufficient condition for it to be true is that each f ∈ T̃S can be approximated by elements of MS in the sense that there exists an element q ∈ R[X ] such that, for ...
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Let f be a piecewise analytic (but not analytic) function in @[a, b], k > 0, and let p,* be the sequence of polynomials of best uniform approximation to f on [a, b]. It is well known that every point of [a, b] is a limit point of the zeros of the p,*. Let x E [a, b], and suppose that f is analytic at x and f(x) # 0. The main purpose of this paper is to show that there exists a constant y (which...
متن کاملFormal Verification of Medina's Sequence of Polynomials for Approximating Arctangent
The verification of many algorithms for calculating transcendental functions is based on polynomial approximations to these functions, often Taylor series approximations. However, computing and verifying approximations to the arctangent function are very challenging problems, in large part because the Taylor series converges very slowly to arctangent—a 57th-degree polynomial is needed to get th...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.2307/2034978