Accurate Computation of Divided Differences of the Exponential Function

Accurate Inference for the Mean of the Poisson-Exponential Distribution

Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

Functionals of exponential Brownian motion and divided differences

We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and its time average, and we find the use of divided differences greatly elucidates formulae, providing a path to several new results. As applicatio...

Exponential Riesz bases of subspaces and divided differences

Linear combinations of exponentials e iλ k t in the case where the distance between some points λ k tends to zero are studied. D. Ull-rich [30] has proved the basis property of the divided differences of exponentials in the case when {λ k } = Λ (n) and the groups Λ (n) consist of equal number of points all of them are close enough to n, n ∈ Z. We have generalized this result for groups with arb...

Accurate and efficient matrix exponential computation

Fast computation of divided differences and parallel hermite interpolation

We present parallel algorithms for fast polynomial interpolation. These algorithms can be used for constructing and evaluating polynomials interpolating the function values and its derivatives of arbitrary order (Hermite interpolation). For interpolation, the parallel arithmetic complexity is 0(log2 M + log N) for large M and N, where M 1 is the order of the highest derivative information and N...