منابع مشابه
The Arithmetic - Harmonic Mean
Consider two sequences generated by ",,+ i Mi"„<hn)hn*\ M'i"„+X,b„), where the a„ and b„ are positive and M and M' are means. The paper discusses the nine processes which arise by restricting the choice of M and M' to the arithmetic, geometric and harmonic means, one case being that used by Archimedes to estimate it. Most of the paper is devoted to the arithmetic-harmonic mean, whose limit is e...
متن کاملSome More Inequalities for Arithmetic Mean, Harmonic Mean and Variance
We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds for the largest and smallest eigenvalues of a positive definite matrix are also obtained.
متن کاملAn Arithmetic-Geometric-Harmonic Mean Inequality Involving Hadamard Products
Given matrices of the same size, A = a ij ] and B = b ij ], we deene their Hadamard Product to be A B = a ij b ij ]. We show that if x i > 0 and q p 0 then the n n matrices q j # are positive deenite and relate these facts to some matrix valued arithmetic-geometric-harmonic mean inequalities-some of which involve Hadamard products and others unitarily invariant norms. It is known that if A is p...
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In this paper, the computation of numerical integration using arithmetic mean (AMDCNC), geometric mean (GMDCNC) and harmonic mean (HMDCNC) derivativebased closed Newton cotes quadrature rules are compared with the existing closed Newton cotes quadrature rule (CNC). The comparison shows that, arithmetic mean-based rule gives better solution than the other two rules. This set of quadrature rules ...
متن کاملBounds for the Arithmetic Mean in Terms of the Neuman, Harmonic and Contraharmonic Means
SB (a, b) = { √ b2−a2 cos−1(a/b) , a < b , √ a2−b2 cosh−1(a/b) , a > b . In this paper, we find the greatest values α1, α2, α3 and α4, and the least values β1, β2, β3 and β4 such that the double inequalities α1SAH(a, b) + (1 − α1)C(a, b) < A(a, b) < β1SAH(a, b) + (1 − β1)C(a, b), α2SHA(a, b) + (1 − α2)C(a, b) < A(a, b) < β2SHA(a, b) + (1 − β2)C(a, b), α3SCA(a, b) + (1 − α3)H(a, b) < A(a, b) < β...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1984
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1984-0725993-3