Related papers: An analog of the Sinc approximation for periodic f…
We create a new, functional calculus, approach to approximation of C_0-semigroups on Banach spaces. As an application of this approach, we obtain optimal convergence rates in classical approximation formulas for C_0-semigroups. In fact, our…
We prove the existence of entire functions that achieve universal approximations on certain countable sequences of translation operators .
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.
We establish interpolation analogues of Lebesgue type inequalities on the sets of $C^{\psi}_{\beta}L_{1}$ $2\pi$-periodic functions $f$, which are representable as convolutions of generating kernel $\Psi_{\beta}(t) =…
The reciprocal function, 1/x, is important for many real-time algorithms. It is used in a large variety of algorithms from areas ranging from iterative estimation to machine learning. Many of these algorithms are iterative in nature and…
The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing…
In this paper, we use some standard numerical techniques to approximate the hypergeometric function $$ {}_2F_1[a,b;c;x]=1+\frac{ab}{c}x+\frac{a(a+1)b(b+1)}{c(c+1)}\frac{x^2}{2!}+\cdots $$ for a range of parameter triples $(a,b,c)$ on the…
Sparse interpolation} refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now…
For a nonempty compact subset $\sigma$ in the plane, the space $AC(\sigma)$ is the closure of the space of complex polynomials in two real variables under a particular variation norm. In the classical setting, $AC[0,1]$ contains several…
Spline quasi-interpolation (QI) is a general and powerful approach for the construction of low cost and accurate approximations of a given function. In order to provide an efficient adaptive approximation scheme in the bivariate setting, we…
A new computational framework for evaluation of the gamma function $\Gamma(z)$ over the complex plane is developed. The algorithm is based on interpolation by rational functions, and generalizes the classical methods of Lanczos…