The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in I1 provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is s...

Pseudo-absences, pseudo-models and pseudo-niches: pitfalls of model selection based on the area under the curve Duncan Golicher a b , Andrew Ford b , Luis Cayuela c & Adrian Newton b a El Colegio de la Frontera Sur, Conservación de la Biodiversidad, San Cristóbal de las Casas, Mexico b Applied Sciences, Bournemouth University, Bournemouth, UK c Área de Biodiversidad y Conservación, Universidad ...

In the Laurent expansion ζ(s, a) = 1 s− 1 + ∞ ∑ k=0 (−1)γk(a) k! (s− 1) , 0 < a ≤ 1, of the Riemann-Hurwitz zeta function, the coefficients γk(a) are known as Stieltjes, or generalized Euler, constants. [When a = 1, ζ(s, 1) = ζ(s) (the Riemann zeta function), and γk(1) = γk.] We present a new approach to high-precision approximation of γk(a). Plots of our results reveal much structure in the gr...

We show how ideas originating in the theory of dynamical systems inspire a new approach to numerical integration of functions. Any Lebesgue integral can be approximated by a sequence of integrals with respect to equidistributions, i.e. evenly weighted discrete probability measures concentrated on an equidistributed set. We prove that, in the case where the integrand is real analytic, suitable l...

2. Write a Matlab script of no more than 10 lines to calculate the Newton-Cotes quadrature weights wj , j = 1, 2, . . . , n, n + 1; go to the end of this handout for more details about wj . For uniformity, we require that the script starts with the four lines n=2; h=1/n; nodes=(0:h:1)’; f=eye(n+1); where the j-th column of the matrix f are needed for the Lagrange interpolation in order to find ...

The main purpose of this paper is to examine the effectiveness of the Quarter-Sweep Gauss-Seidel (QSGS) method in solving the dense linear systems generated from the discretization of the linear Fredholm integral equations of the second kind. In addition, the applications of the various orders of closed Newton-Cotes quadrature discretization schemes will be investigated in order to form linear ...

and hosti 013.02.0 Abstract A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear ...

For the unit sphere embedded in a Euclidean space, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered points (sites). The number of scattered sites required is comparable to the dimension of the space for which the quadrature formula is required to be exact. As a part of the proof, we der...