Sentence examples for the power basis from inspiring English sources

where b ij are the coefficients of the power basis that are used to determine the respective Bernoulli polynomials.

These algorithms are only then of practical importance if they do not require the ill-conditioned conversion between the Bernstein and the power basis.

On the other hand, the conversion between the Bernstein and the power basis is ill conditioned, thus only the degree reduction algorithms which may be carried out without using this conversion are of practical value.

Any Bernstein polynomial of degree n can be written in terms of the power basis directly calculated by using the binomial expansion of 1-x ^{n-i}i}) as follows: B_{i,n}(x)= sum_{j=i}^{n} (-1-x ^{n-i}inom{n}{i} binom{n-i}{j-i} x^{j},quad i=0,ldots,n.

A series of numerical tests are reported and discussed, which indicate that Bernstein Bezoutian matrices are much less sensitive to perturbations of the coefficients of the input polynomials compared to other commonly used resultant matrices generated after having performed the explicit conversion between the Bernstein and the power basis.

In the case of an Amerasian call option, for example, we find that the preferable polynomial basis is Hermite A. For an Amerasian put option, the Power polynomial basis is recommended.

Considering the outstanding properties of the NS-power basis which was given by Sánchez-Reyes in 1997, the dual basis functions for the NS-power basis are presented in this paper.

Applying the method leads to a set of linear algebraic equations to solve for the unknown weighting coefficients for the power series basis terms.

The news has recently hit the press that China's economy, measured on the purchasing-power basis that adjusts for price differences between nations, may surpass the U.S. in only another five years or so.

32 We used appropriate equations to estimate the power, on the basis of whether the largest study reported a hazard ratio or an odds ratio.

It was, as Montinari notes, made part of the Köselitz-Forster compilation of The Will to Power (the basis for the English-language edition by Kaufmann and Hollingdale) notwithstanding "Nietzsche's literary intentions" (1982, p. 104).