Chisini mean
Encyclopedia
In mathematics
, a function f of n variables
leads to a Chisini mean M if for every vector <x1 ... xn>, there exists a unique M such that
The arithmetic
, harmonic
, geometric
, generalised, Heronian and quadratic means are all Chisini means, as are their weighted variants.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a function f of n variables
- x1, ..., xn
leads to a Chisini mean M if for every vector <x1 ... xn>, there exists a unique M such that
- f(M,M, ..., M) = f(x1,x2, ..., xn).
The arithmetic
Arithmetic mean
In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
, harmonic
Harmonic mean
In mathematics, the harmonic mean is one of several kinds of average. Typically, it is appropriate for situations when the average of rates is desired....
, geometric
Geometric mean
The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, except that the numbers are multiplied and then the nth root of the resulting product is taken.For instance, the...
, generalised, Heronian and quadratic means are all Chisini means, as are their weighted variants.