In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fréchet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild cond...

All the confirmed Soft Gamma-ray Repeaters have been observed with the EPIC instrument on the XMM– Newton satellite. We review the results obtained in these observations, providing the most accurate spectra on the persistent X-ray emission in the 1–10 keV range for these objects, and discuss them in the context of the magnetar interpretation.

The dynamical effect of the cosmological constant Λ on a single spherical void evolving in a Friedmann-Lemâıtre universe is investigated within a non linear perturbation of Newton-Friedmann models. The void expansion shows a huge initial burst, which freezes asymptotically up to match Hubble expansion. Λ-effect on the kinematics intervenes significantly by amplifying the expansion rate at redsh...

Peer two-step methods have been successfully applied to initial value problems for stiff and non-stiff ordinary differential equations both on parallel and sequential computers. Their essential property is the use of several stages per time step with the same accuracy. As a new application area these methods are now used for parameter-dependent ODEs where the peer stages approximate the solutio...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

In this paper we present a new algehrwic analysis of the closure equation obtained for arbitrary single loop spatial kinematic chains, which allows us to design an eficient interval method for solving their inverse kinematics. The solution of a kinematic equation can be factored into a solution of both its rotational and its translational components. We have obtained general and simple expressi...

Fractional directional integrals are the extensions of the Riemann-Liouville fractional integrals from oneto multi-dimensional spaces and play an important role in extending the fractional differentiation to diverse applications. In numerical evaluation of these integrals, the weakly singular kernels often fail the conventional quadrature rules such as Newton-Cotes and Gauss-Legendre rules. It ...

We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering meth...

Numerical solutions to partial differential equations form the backbone of mathematical models that simulate the behavior of various electrochemical systems, specifically, batteries and fuel cells. In this paper, we present a set of numerical algorithms applied to efficiently solve this system of equations. These fast algorithms are identified by fully understanding the physics of the problem a...