This report presents several approaches aimed at reducing the bias and uncertainty of the free energy difference estimates obtained using the thermodynamic integration simulation strategy. The central idea is to utilize interpolation schemes, rather than the often-used trapezoidal rule quadrature, to fit the thermodynamic integration data, and obtain a more accurate and precise estimate of the ...

In a multi-secret sharing scheme, several secret values are distributed among a set of n participants.In 2000 Chien et al.'s proposed a (t; n) multi-secret sharing scheme. Many storages and publicvalues required in Chien's scheme. Motivated by these concerns, some new (t; n) multi-secret sharingschemes are proposed in this paper based on the Lagrange interpolation formula for polynomials andcip...

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The solution takes the form product consisting unknown coefficients and polynomials. Our main task is compute numerical values coefficients. To achieve goal, apply initial condition problem, Tau Lagrange multiplier methods. We do error ana...

In this note we prove mean convergence of Lagrange interpolation at the zeros para-orthogonal polynomials for measures on unit circle which do not belong to Szegő’s class. When measure is in class, proved functions disk algebra.

Minimal degree interpolation spaces with respect to a nite set of points are subspaces of multivariate polynomials of least possible degree for which Lagrange interpolation with respect to the given points is uniquely solv-able and degree reducing. This is a generalization of the concept of least interpolation introduced by de Boor and Ron. This paper investigates the behavior of Lagrange inter...

where > 0. Once the theory had been developed in its entirety, it became clear that one could simultaneously treat not only weights like those above, but also not necessarily even weights on a general real interval. See [3], [12], [16] for various perspectives on this type of potential theory and its applications. One important application is to Lagrange interpolation. Mean convergence of Lagra...

In 1918 Bernstein [2] published a result concerning the divergence of Lagrange interpolation based on equidistant nodes. This result, which now has a prominent place in the study of the appoximation of functions by interpolation polynomials, may be described as follows. Throughout this paper let / (* ) = |x| (—1 < x < 1) and Xk,n = 1 + 2(fcl ) / ( n l ) (Jfe = 1,2,... ,n; n = 1 ,2 ,3 , . . . ) ...

It is known that for Pn, the subspace of C([−1, 1]) of all polynomials of degree at most n, the least basis condition number κ∞(Pn) (also called the Banach-Mazur distance between Pn and `n+1 ∞ ) is bounded from below by the projection constant of Pn in C([−1, 1]). We show that κ∞(Pn) is in fact the generalized interpolating projection constant of Pn in C([−1, 1]), and is consequently bounded fr...