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Good's formula and Fisher's method are frequently used for combining independent P-values. Interestingly, the equivalent of Good's formula already emerged in 1910 and mathematical expressions relevant to even more general situations have…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the…
Approximations of non-smooth multivariate functions return low-order approximations in the vicinities of the singularities. Most prior works solve this problem for univariate functions. In this work we introduce a method for approximating…
We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the…
Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…
We show how one can obtain an asymptotic expression for some special functions satisfying a second order differential equation with a very explicit error term starting from appropriate upper bounds. We will work out the details for the…
Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on…
The probability density function of the random flight with isotropic initial conditions is obtained by an expansion in the number of collisions and the in the spatial harmonics of the solution, as in a Fourier series. The method holds for…
This paper is devoted to a new first order Taylor-like formula where the corresponding remainder is strongly reduced in comparison with the usual one which appears in the classical Taylor's formula. To derive this new formula, we introduce…
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…
The distributions of the $k$-th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and their numerical evaluation is a subject of great practical…
In this work we propose a generalized additive functional regression model for partially observed functional data. Our approach accommodates functional predictors of varying dimensions without requiring imputation of missing observations.…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
In our recent research endeavors, we have delved into the realm of tail bounds problems concerning bivariate random tensor means. In this context, tensors are treated as finite-dimensional operators. However, the longstanding challenge of…
We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called…
We present in this paper first-order alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most $O(1/\epsilon)$…
Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/\pi$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…