Construction of Gauss quadratures with prescribed knots via Jacobi matrices is extended to the case where not all orthogonal polynomials exist due to the weight function changing sign. An algorithm is described and is demonstrated by calculating the knots of Kronrod schemes and other Gauss quadratures with prescribed knots.

We review the methods in [4] and [24] for constructing quadratures for bandlimited exponentials and introduce a new algorithm for the same purpose. As in [4], our approach also yields generalized Gaussian quadratures for exponentials integrated against a non-sign-definite weight function. In addition, we compute quadrature weights via l and l∞ minimization and compare the corresponding quadratu...

Highly efficient quantum dense coding for continuous variables has been experimentally accomplished by means of exploiting bright EPR beam with anticorrelation of amplitude quadratures and correlation of phase quadratures, which is generated from a nondegenerate optical parametric amplifier operating in the state of deamplification. Two bits of classical information are encoded on two quadratur...

The paper reviews the relation between Padé-type approximants of a power series and interpolatory quadrature formulas with free nodes, and that between Padé approximants and Gaussian quadrature methods. Quadrature methods are well-known. They are used for obtaining an approximate value of a definite integral, and are described in any book of numerical analysis. In this talk, we will show that P...

The Gaussian integration of moments is systematically discussed. It is shown that the well-known diffusivityfactor approximation is equivalent to a one-node Gaussian quadrature. The limit as the moment power approaches infinity in a one-node Gaussian quadrature produces a diffusivity factor of e1/2 5 1.648 721 3, which is very close to the value of 1.66 suggested by Elsasser. The errors due to ...

The calculation of quadratures arises in many physical and technical applications. replacement integration variables is proposed, which dramatically increases the accuracy formula averages. For infinitely smooth integrand functions, convergence law becomes super power. It significantly faster than power close to exponential one. integrals with bounded smoothness, realized maximum achievable ord...

This article is concerned with Bayesian estimation of parameters in non-linear multivariate stochastic differential equation (SDE) models occurring, for example, in physics, engineering, and financial applications. In particular, we study the use of adaptive Markov chain Monte Carlo (AMCMC) based numerical integration methods with nonlinear Kalman-type approximate Gaussian filters for parameter...

Two methods of discrete images are proposed to approximate the reaction field from ionic solvent for a point charge inside a dielectric spherical cavity. Fast and accurate calculation of such a reaction field is needed in hybrid explicit/implicit solvation models of biomolecules. A firstand a second-order image approximation methods, in the order of u = λa (λ – the inverse Debye screening lengt...