Extended convergence analysis of Newton-Potra solver for equations

In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839.... The radius of the convergence ball and convergence order of the investigated solver are determined in an earlier paper. Modifications of previous conditions leads to extended convergence domain. These advantages are obtained under the same computational effort. Numerical experiments are carried out on the test examples with nondifferentiable operator

Improved Convergence Analysis of Gauss-Newton-Secant Method for Solving Nonlinear Least Squares Problems

We study an iterative differential-difference method for solving nonlinear least squares problems, which uses, instead of the Jacobian, the sum of derivative of differentiable parts of operator and divided difference of nondifferentiable parts. Moreover, we introduce a method that uses the derivative of differentiable parts instead of the Jacobian. Results that establish the conditions of convergence, radius and the convergence order of the proposed methods in earlier work are presented. The numerical examples illustrate the theoretical results

Extended convergence analysis of Newton-Potra solver for equations

In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839.... The radius of the convergence ball and convergence order of the investigated solver are determined in an earlier paper. Modifications of previous conditions leads to extended convergence domain. These advantages are obtained under the same computational effort. Numerical experiments are carried out on the test examples with nondifferentiable operator

Gene Expression Regulation and Secretory Activity of Mesenchymal Stem Cells upon In Vitro Contact with Microarc Calcium Phosphate Coating

The manufacture of biomaterial surfaces with desired physical and chemical properties that can directly induce osteogenic differentiation without the need for biochemical additives is an excellent strategy for controlling the behavior of mesenchymal stem cells (MSCs) in vivo. We studied the cellular and molecular reactions of MSCs to samples with a double-sided calcium phosphate (CaP) coating and an average roughness index (Ra) of 2.4–4.6 µm. The study aimed to evaluate the effect of a three-dimensional matrix on the relative mRNA expression levels of genes associated with the differentiation and maturation of MSCs toward osteogenesis (RUNX2, BMP2, BMP6, BGLAP, and ALPL) under conditions of distant interaction in vitro. Correlations were revealed between the mRNA expression of some osteogenic and cytokine/chemokine genes and the secretion of cytokines and chemokines that may potentiate the differentiation of cells into osteoblasts, which indicates the formation of humoral components of the extracellular matrix and the creation of conditions supporting the establishment of hematopoietic niches