This appendix contains the proof of Theorem 2 which is the main result for the general version of the model presented in Section II of the paper. The numbering here (of equations, result, and definitions, etc.) follows the numbering in the published paper. Assumptions 6-10, which are stated in the paper, are assumed implicitly throughout. A single subscript will be used to denote the number of ...

We study the rate of convergence of Wilkinson’s shift iteration acting on Jacobi matrices with simple spectrum. We show that for AP-free spectra (i.e., simple spectra containing no arithmetic progression with 3 terms), convergence is cubic. In order 3, there exists a tridiagonal symmetric matrix P0 which is the limit of a sequence of a Wilkinson iteration, with the additional property that all ...

the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

Abstract In recent years, researchers have studied the use of different iteration processes from fixed point theory in generation complex fractals. For instance, Mann, Ishikawa, Noor, Jungck–Mann and Jungck–Ishikawa iterations been used. this paper, we study Picard–Mann with s -convexity Mandelbrot Julia sets. We prove escape criterion for $$(k+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

In the beginning of the eighties, M. Shub and S. Smale developed a quantitative analysis of Newton’s method for multivariate analytic maps. In particular, their α-theory gives an effective criterion that ensures safe convergence to a simple isolated zero. This criterion requires only information concerning the map at the initial point of the iteration. Generalizing this theory to multiple zeros...

This paper proposes a dual-iterative method, a hierarchical inner and outer iteration method (HIO), to acquire concept words from a large-scale, un-segmented Chinese corpus. It has two levels of iteration: the EM-CLS algorithm and the Viterbi-C/S algorithm constitute the inner iteration for generating concept words, and the concept word validation constitutes the outer iteration together with t...

Using finite support iteration of c.c.c. partial orders we provide a model of b = κ < s = κ for κ an arbitrary regular, uncountable cardinal.

In this paper, we apply the Newton’s and He’s iteration formulas in order to solve the nonlinear algebraic equations. In this case, we use the stochastic arithmetic and the CESTAC method to validate the results. We show that the He’s iteration formula is more reliable than the Newton’s iteration formula by using the CADNA library.

The purpose of this article is to initiate the notion monotone multivalued generalized (α,β)-nonexpansive mappings and explore iterative approximation fixed points for mapping in an ordered CAT(0) space. In particular, we employ S-iteration algorithm space prove some convergence results. Moreover, examples useful results related proposed are provided. Numerical experiments also provided illustr...

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎‎direct iteration methods for solving a linear system where the‎‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎‎rank linear equations‎, ‎w...