In this paper we propose an extension of the iteratively regularized Gauss– Newton method to the Banach space setting by defining the iterates via convex optimization problems. We consider some a posteriori stopping rules to terminate the iteration and present the detailed convergence analysis. The remarkable point is that in each convex optimization problemwe allow non-smooth penalty terms inc...

A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the three-term recurrence relation satisfied by the orthogonal polynomials. Once these are known, additional data can be generated, such as z...

We consider some time-changed diffusion processes obtained by applying the Doob transformation rule to a Brownian motion. The time-change is via inverse of an α-stable subordinator. These are specified in terms Gauss-Markov and fractional diffusions. A pseudo-Fokker-Planck equation for such given. investigate their first passage time densities providing generalized integral they satisfy rules. ...

The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs and the beauty of these classical resul...

Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependen...

This paper investigates the role of quadrature exactness in approximation scheme hyperinterpolation. Constructing a hyperinterpolant degree $n$ requires positive-weight rule with $2n$. We examine behavior such when required $2n$ is relaxed to $n+k$ $0<k\leq n$. Aided by Marcinkiewicz--Zygmund inequality, we affirm that $L^2$ norm exactness-relaxing hyperinterpolation operator bounded constant i...

In this work, a joint quadrature for numerical solution of the double integral is presented. This method based on combining two rules same precision level to form higher precision. Numerical results present with lower are presented and compared those performed by existing high-precision Gauss-Legendre five-point rule in variables, which has functional evaluation. The efficiency proposed justifi...

We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG...

Ferrofluid instabilities in DC magnetic fields for an Isopar-M based ferrofluid with saturation magnetization of about 400 Gauss. a) 1200 Gauss 5 mm diameter magnet behind small ferrofluid droplet surrounded by propanol to prevent ferrofluid wetting of 1 mm gap glass plates; Peak pattern with magnetic field perpendicular to ferrofluid layer. The peaks initiate in a hexagonal array when the magn...