Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...

A linear algebra proof is given of the fact that the nullspace of a finite-rank linear projector, on polynomials in two complex variables, is an ideal if and only if the projector is the bounded pointwise limit of Lagrange projectors, i.e., projectors whose nullspace is a radical ideal, i.e., the set of all polynomials that vanish on a certain given finite set. A characterization of such projec...

In this paper, we apply and compare modified Variational Iteration Methods (VIMAP) to find travelling wave solutions of Whitham-Broer-Kaup (WBK) equations. The proposed modifications are made by introducing Adomian’s and He’s polynomials in the correction functional of the VIM. The use of Lagrange multiplier coupled with He’s polynomials explicitly reveal a clear edge over the coupling with Ado...

In this work we suggest a new approach to the determination of new identities for Bell’s polynomials, based on the Lagrange inversion formula, and the binomial sequences. This approach allows the easy recovery of known identities and deduction of some new identities including these polynomials.

In this paper, we present some miscellaneous properties of the multivariable Humbert polynomials whose special cases include some well-known multivariable polynomials such as Chan-Chyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We give recurrence relations, addition formula and integral representation for them. Then, we obtain some partial differential equatio...

Symmetric functions can be considered as operators acting on the ring of polynomials with coeecients in R. We present the package SFA, an implementation of this action for the computer algebra system Maple. As an example, we show how to recover diierent classical expressions of Lagrange inversion, and of Faber polynomials.

Division algorithms for univariate polynomials represented with respect to Lagrange and Bernstein basis are developed. These algorithms are obtained by abstracting from the classical polynomial division algorithm for polynomials represented with respect to the usual power basis. It is shown that these algorithms are quadratic in the degrees of their inputs, as in the power basis case.

In this work, we propose two new methods for the determination of new identities for Bell’s polynomials. The first method is based on the Lagrange inversion formula, and the second is based on the binomial sequences. These methods allow the easy recovery of known identities and deduction of some new identities of these polynomials. © 2005 Elsevier B.V. All rights reserved. MSC: 05A16