Equidistributed is a property of a bounded sequence of numbers. If equidistributed, then each point in the sequence is equally likely to fall anywhere in its range. For comparison, see Poisson distribution and normal distribution. In probability theory and statistics, the Poisson distribution is a discrete probability distribution (discovered by Siméon-Denis Poisson (1781–1840) and published, together with his probability theory, in 1838 in his work Recherches sur la probabilité des jugements en matières criminelles et matière civile) belonging to certain random variables N... The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields, especially in physics and engineering. ...
In analytic number theory, the fractional parts of the sequences and are equidistributed in the interval [0,1) for all irrational (where the coefficients in the second sequence are the primes), the latter result being a famous theorem of Vinogradov. Analytic number theory is the branch of number theory that uses methods from mathematical analysis. ... In mathematics, a prime number, or prime for short, is a natural number greater than one and whose only distinct positive divisors are 1 and itself. ... Ivan Matveevich Vinogradov (September 14, 1891–March 20, 1983) was a Russian mathematician, who was one of the creators of modern analytic number theory, and also the dominant figure in mathematics in the USSR. He was born in the Velikiye Luki district, Pskov Oblast. ...
The polynomial interpolation on a quasi-equidistributed node set which is a union of several rotations around the origin for an equidistributed node set on the unit circle is investigated.
A scheme for generating a sequence of quasi-equidistributed node sets for polynomial interpolation on the unit disk is proposed, in which each set is contained in its successor and the average increased rate of number of nodes at each step is less than 2, in fact, may be arbitrarily close to 1.
Our interpolation process is as stable as the ordinary process on equidistributed node sets, since the Lebesgue constant of the corresponding interpolation has a logarithmic rate of growth and the (spectral) condition number of the finite dimensional linear transformation, from the sample values to the coefficients of the interpolation polynomial, is bounded.
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