We study the local convergence properties of inexact Newton-Gauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved.

An algorithm is described for the efficient numerical solution of singular two-point boundary value problems. The algorithm is based on collocation at Gauss points, is applied directly to second order equations and uses a transformation of the independent variable to obtain extra smoothness if needed. Numerical comparisons between a code based on this approach and codes based on other options w...

This paper addresses the development of a new algorithm for parameter estimation of ordinary differential equations. Here, we show that (1) the simultaneous approach combined with orthogonal cyclic reduction can be used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints without the need for structural information to devise a stable embe...

The problem of recovering a parameter function based on measurements of solutions of a system of partial diierential equations in several space variables leads to a number of computational challenges. Upon discretization of a regularized formulation a large, sparse constrained optimization problem is obtained. Typically in the literature , the constraints are eliminated and the resulting uncons...

We derive a simple accuracy matching strategy for inexact Gauss Newton methods and apply it to the numerical solution of boundary value problems of ordinary differential equations by collocation. The matching strategy is based on an affine contravariant convergence theorem, i.e., the characteristic constants are invariant under affine transformations of the domain. The inexact Gauss Newton meth...

Of all the traditional (or Greek) centers of a triangle, the orthocenter (i.e., the point of concurrence of the altitudes) is probably the one that attracted the most of attention. This may be due to the fact that it is the only one that has no exact analogue for arbitrary higher dimensional simplices, for spherical and hyperbolic triangles, or for triangles in normed planes. But it possibly ha...

Corrections to solar system gravity are derived for f(G) gravity theories, in which a function of the Gauss-Bonnet curvature term is added to the gravitational action. Their effects on Newton’s law, as felt by the planets, and on the frequency shift of signals from the Cassini spacecraft, are both determined. Despite the fact that the Gauss-Bonnet term is quadratic in curvature, the resulting c...