Related papers: New Interval Calculus with Application to Interval…
Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
In this article, the notion of gH-Clarke derivative for interval-valued functions is proposed. To define the concept of gH-Clarke derivatives, the concepts of limit superior, limit inferior, and sublinear interval-valued functions are…
The purpose of this paper is to prove an interpolation formula involving derivatives for entire functions of exponential type. We extend the interpolation formula derived by J. Vaaler in [37, Theorem 9] to general $L^p$ de Branges spaces.…
Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality…
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex…
The interval numbers is the set of compact intervals of $\mathbb{R}$ with addition and multiplication operation, which are very useful for solving calculations where there are intervals of error or uncertainty, however, it lacks an…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
In this note we define and study a Hilbert space-valued stochastic integral of operator-valued functions with respect to Hilbert space-valued measures. We show that this integral generalizes the classical Ito stochastic integral of adapted…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…