Least-squares fitting of circles and ellipses.
Local convergence analysis of a modified Newton-Jarratt's composition under weak conditions
A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces
We present a local convergence analysis of a one parameter Jarratt-type method. We use this method to approximate a solution of an equation in a Banach space setting. The semilocal convergence of this method was recently carried out in earlier studies under stronger hypotheses. Numerical examples are given where earlier results such as in [Ezquerro J.A., Hernández M.A., New iterations of -order four with reduced computational cost, BIT Numer. Math. 49 (2009), 325–342] cannot be used to solve equations...
Localized polynomial bases on the sphere.
Lösung von Differentialgleichungen mit Splinefunktionen. Eine Störungstheorie. Tei 1: Divergenzaussagen.
Multidimensional smoothing using hyperbolic interpolatory wavelets.
Nonlinear approximation in control problems
Numerische Methoden zur Behandlung einiger Problemklassen der nichtlinearen Tschebyscheff-Approximation mit Nebenbedingungen.
Numerische Polynomapproxiamtion mit Knotenpolynomen.
On an iterative method for unconstrained optimization
We present a local and a semi-local convergence analysis of an iterative method for approximating zeros of derivatives for solving univariate and unconstrained optimization problems. In the local case, the radius of convergence is obtained, whereas in the semi-local case, sufficient convergence criteria are presented. Numerical examples are also provided.
On one approach to local surface smoothing
A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
On Orthogonal Linear ...1 Approximation.
On the Remez Algorithm for Non-linear Families.
On the smoothing spline regression models.
Optimal Approximation and Error Bounds in Seminormed Spaces.
Optimale Quadraturformeln mit semidefiniten Peano-Kernen. - Optimal Integration Formulas with Semidefinite Peano-Kernels.
Orthogonal Least Squares Fitting with Linear Manifolds.
Orthonormal polynomial vectors and least squares approximation for a discrete inner product.
Perturbations of Best Approximation Problems.
Polynomials associated with exponential regression
Fitting exponentials to data by the least squares method is discussed. It is shown how the polynomials associated with this problem can be factored. The closure of the set of this type of functions defined on a finite domain is characterized and an existence theorem derived.