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When extending the Ehrhart lattice point enumerator $L_P(t)$ to allow real dilation parameters $t$, we lose the invariance under integer translations that exists when $t$ is restricted to be an integer. This paper studies this phenomenon;…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
We consider the asymptotic expansion of the Wright function \[W_{\lambda,\mu}(z)=\sum_{n=0}^\infty\frac{z^n}{n! \Gamma(\lambda n+\mu)}\qquad (\lambda>-1)\] for large (positive and negative) variable and large parameter $\mu$. The analysis…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
In this paper we consider a step function characterized by an arbitrary sequence of real-valued scalars and approximate it with a matching pursuit (MP) algorithm. We utilize a waveform dictionary with rectangular window functions as part of…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear operator. The iterative schemes are formulated in the spirit…
The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…
Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that…
An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
Value-function approximation methods that operate in batch mode have foundational importance to reinforcement learning (RL). Finite sample guarantees for these methods often crucially rely on two types of assumptions: (1) mild distribution…
We establish an effective improvement on the Liouville inequality for approximation to complex non-real algebraic numbers by quadratic complex algebraic numbers.
The objective of this publication is to reduce the sensitivity of iterative equation solvers on the initial value. To this end, at the hand of Newton's method, we exemplify how to reformulate the initial problem by means of a set of…
In this paper we propose a method for computing the Faddeeva function $w(z) := e^{-z^2}\mathrm{erfc}(-i z)$ via truncated modified trapezoidal rule approximations to integrals on the real line. Our starting point is the method due to Matta…
An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq…