Related papers: A product integration rule on equispaced nodes for…
In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent…
We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable $v$ on the skew product to an observable…
We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved elements. Although high order, the precision of the…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
We present a design framework to induce stable oscillations through mixed feedback control. We provide conditions on the feedback gain and on the balance between positive and negative feedback contributions to guarantee robust oscillations.…
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning of the input. However, in the context of a non-standard inner product, it becomes difficult…
A comprehensive linear stability analysis of force-gradient integrators and their Hessian-free variants is carried out by investigating the harmonic oscillator as a test equation. The analysis reveals that the linear stability of…
In this paper, we will study a class of linear integral operators with the nonnegative kernels on higher-dimensional product spaces, the norms of the operators can be obtained by integral of the product of the kernel function and finitely…
Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.
In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a rigorous curve following argument build on high order…
We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme.…
In this work, we present and analyze the numerical stability of two coupled finite element formulations. The first one is the h-a-formulation and is well suited for modeling systems with superconductors and ferromagnetic materials. The…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
In this paper we present a new family of rules for numerical integration. This family has up to half the error of the widely used Newton-Cotes rules when a sufficient number of points is evaluated and also much better numerical stability…
The paper reports on a study of a harmonic oscillator (ho) in the twisted Moyal space, in a well defined matrix basis, generated by the vector fields…
Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations…