Noun1.geometric mean- the mean of n numbers expressed as the n-th root of their product statistics- a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters ...
Summary The geometric mean of two matrices is considered from a computational viewpoint. Several numerical algorithms based on different properties and representations of the geometric mean are discussed and analyzed. It is shown that most of the algorithms can be classified in terms of the rational...
is that the arithmetic mean tends to overstate the actual average return by a greater and greater amount the more the inputs vary. In Example 2, the returns increased by 10% in year one, 150% in year two and then decreased by 30% in year 3. This is an increase of 130% from the ...
The paper is thus an excellent self-contained tutorial on the theory of the arithmetic-geometric mean, quadratically convergent algorithms (including Newton's algorithm for computing square roots and roots of polynomials), and how these concepts lead to fast algorithms for π and elementary functions...
To account for spatial offsets, previously an arithmetic mean of the time-domain fields to either side of the integration boundary has been used. Here we show that superior results are obtained by instead using a geometric mean of the harmonic fields to either side of the integration boundary....
Let pn denote the n-th prime number and let Gn be the geometric mean of the first n primes. It is well-known that Gn/pn → 1/e as n →∞, where e is the Euler's number. The aim of this note is to give various proofs of this fact, equivalent establishments and generalizations....
Formulas are derived, by direct integration of the defining definite integrals, for the general geometric mean distance between (i) a point and a line segment; (ii) a point and a rectangular area; (iii) two parallel line segments; (iv) two orthogonal line segments; (v) a line segment an...
The development of this algorithm involves a proof that the portfolio with maximum geometric mean lies on the efficient frontier in arithmetic mean variance space. This finding has major implications for the relevancy of much of portfolio and general equilibrium theory. These implications are explored....
PATHFINDER-STATISTICS AND MATHEMATICAL REASONING-QUESTION BANK The mean of first three terms is 14 and mean of next two terms is 18. ... 04:13 Geometric mean of the numbers 2, 2^2, 2^3, ….,2^(n) numbers is 04:04 The geometric mean of numbers observations x1, x2, x3,….,xn...
of neural field theories (NFTs)4,5,6that describe mean-field neural dynamics on spatial scales above 0.5 mm (Supplementary Information1). One physiologically constrained form of NFT has unified a diverse range of empirical phenomena6,21by treating cortical activity as a superposition of ...