2 Euclidean Algorithm and Hermite Normal Form 9 2.1 Sizes of Rational Numbers and Polynomial Complexity . . . . . . . . . . . . 9 2.2 Computing the GCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Computing the Hermite Normal Form . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Lattices and the Hermite Normal Form . . . . . . . . . . . . . . . . . . . . . 15 2.5 Dual ...

Standard numerical methods for the Birkhoff-Rott equation for a vortex sheet are unstable due to the amplification of roundoff error by the Kelvin-Helmholtz instability. A nonlinear filtering method was used by Krasny to eliminate this spurious growth of round-off error and accurately compute the Birkhoff-Rott solution essentially up to the time it becomes singular. In this paper convergence is...

We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type decomposition that was obtained from the Baker–Campbell–Hausdorff formula in our study of the Hopf algebra approach of Connes and Kreimer to renormalization ...

In this paper we introduce operator preinvex functions and establish a Hermite–Hadamard type inequality for such functions. We give an estimate of the right hand side of a Hermite–Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved. Also some Hermite–Hadamard type inequalities for the product of two operator preinvex functio...

In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence, and magnitude of errors can be exp...

Biorthogonal multiwavelets are generated from refinable function vectors by using multiresolution analyses. To obtain a biorthogonal multiwavelet, we need to construct a pair of primal and dual masks, from which two refinable function vectors are obtained so that a multiresolution analysis is formed to derive a biorthogonal multiwavelet. It is well known that the order of vanishing moments of a...

We show that the geometric Hermite interpolant can be easily calculated without solving a system of nonlinear equations. In addition we give geometric conditions for the existence and uniqueness of a solution to the interpolation problem. Finally we compare geometric Hermite interpolation with standard cubic Hermite interpolation. x1 Introduction Since parametric representations of curves are n...

An image watermarking scheme that combines Hermite functions expansion and space/spatial-frequency analysis is proposed. In the first step, the Hermite functions expansion is employed to select busy regions for watermark embedding. In the second step, the space/spatialfrequency representation and Hermite functions expansion are combined to design the imperceptible watermark, using the host loca...

The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x, y) is divided into two types: interior point and exterior point. The value of ...

in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...