We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Hermite matrix. If some power of a polynomial admits a de...

Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...

In this paper an approximation of multivariable functions by Hermite basis is presented and discussed. Considered here basis is constructed as a product of one-variable Hermite functions with adjustable scaling parameters. The approximation is calculated via hybrid method, the expansion coefficients by using an explicit, non-search formulae, and scaling parameters are determined via a search al...

A method is presented for the compression of biomedical images using in place of the discrete cosine transform (DCT) the discrete orthogonal Gauss-Hermite transform (DOGHT). The latter expands the signals on a basis of Gauss-Hermite functions instead of the cosine functions and leads, in many practical cases, to 2-3 times better compression for the same reconstruction error as the DCT. This is ...

Existing time-frequency representations are usually too noisesensitive or has too bad resolution for studying multiple transient signal components of biosonar signals. In this paper we calculate reassigned spectrograms using the first Hermite function as window. The optimal length Hermite function giving the perfectly localized reassignment for a Gaussian function is combined with a novel techn...

We propose a general study of the convergence of a Hermite subdivision scheme H of degree d > 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme S. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of S is contractive, then S is C...

Talk Abstract We describe the application of arbitrary-order Hermite methods to hyperbolic-parabolic systems, including parabolic systems as a special case, emphasizing situations where the parabolic terms are small (e.g. large Reynolds or Peclet numbers). Using Fourier methods, we study the dispersion relation for the semidiscretized problem, leading to an understanding of time-step stability ...

This paper presents some asymptotical results of the Hermite Normality test previously introduced. We show that the Hermite statistic S H is distributed under the null hypothesis as a quadratic form of normal variates and under the nonnull hypothesis as normal. The special case of tests with two polynomials is studied in details. Finally, we give some considerations for the choice of a best Her...

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Boltzmann (LB) construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function (EDF) are addressed. A new moment system is proposed. The theoretical possibility to obtain a high-order Hermite-based LB model capable to exactly match some first hydrodynamic momen...

In this study, the Hermite–Hadamard–Fejér inequalities for GA-h-convex are proved, and results particular classes of functions highlighted. addition, several generalizations Hermite–Hadamard presented. Some features H F that naturally linked to Hermite–Hadamard–Fejér-type have also been discussed. Finally, we obtain applications related p-logarithmic mean order p.