Solution of a two-point boundary value model of immobilized enzyme reactions, using an S-system-based root-finding method

2002 ◽  
Vol 127 (2-3) ◽  
pp. 289-310 ◽  
Author(s):  
Fumihide Shiraishi ◽  
Eberhard O. Voit
Keyword(s):  
Immobilized Enzyme ◽  
Boundary Value ◽  
Point Boundary ◽  
Enzyme Reactions ◽  
Root Finding ◽  
Value Model ◽  
Root Finding Method ◽  
Finding Method

Parallel Root-Finding Method for LPC Analysis of Speech

2004 ◽  
pp. 529-536
Author(s):  
Juan-Luis García Zapata ◽  
Juan Carlos Díaz Martín ◽  
Pedro Gómez Vilda
Keyword(s):  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model

2018 ◽  
Vol 301 ◽  
pp. 21-31 ◽  
Author(s):  
Michio Iwata ◽  
Atsuko Miyawaki-Kuwakado ◽  
Erika Yoshida ◽  
Soichiro Komori ◽  
Fumihide Shiraishi
Keyword(s):  
Reaction Model ◽  
Metabolic Reaction ◽  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

scholarly journals Visual Analysis of the Newton’s Method with Fractional Order Derivatives

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1143 ◽  
Author(s):  
Krzysztof Gdawiec ◽  
Wiesław Kotarski ◽  
Agnieszka Lisowska
Keyword(s):  
Visual Analysis ◽  
Dynamic Properties ◽  
Speed Of Convergence ◽  
Polynomial Zeros ◽  
Polynomial Roots ◽  
Root Finding ◽  
Root Finding Method ◽  
Finding Method ◽  
Number Of Iterations ◽  
Basins Of Attractions

The aim of this paper is to investigate experimentally and to present visually the dynamics of the processes in which in the standard Newton’s root-finding method the classic derivative is replaced by the fractional Riemann–Liouville or Caputo derivatives. These processes applied to polynomials on the complex plane produce images showing basins of attractions for polynomial zeros or images representing the number of iterations required to obtain polynomial roots. These latter images were called by Kalantari as polynomiographs. We use both: the colouring by roots to present basins of attractions, and the colouring by iterations that reveal the speed of convergence and dynamic properties of processes visualised by polynomiographs.

scholarly journals A Newton method for harmonic mappings in the plane

2019 ◽  
Vol 40 (4) ◽  
pp. 2777-2801
Author(s):  
Olivier Sète ◽  
Jan Zur
Keyword(s):  
Basins Of Attraction ◽  
Harmonic Mappings ◽  
Iterative Root ◽  
Number Of Solutions ◽  
Critical Set ◽  
Complex Formulation ◽  
Root Finding ◽  
Matlab Implementation ◽  
Root Finding Method ◽  
Finding Method

Abstract We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton’s method for analytic functions. The complex formulation of the method allows an analysis in a complex variables spirit. For zeros close to poles of $f = h + \overline{g}$ we construct initial points for which the harmonic Newton iteration is guaranteed to converge. Moreover, we study the number of solutions of $f(z) = \eta $ close to the critical set of $f$ for certain $\eta \in \mathbb{C}$. We provide a MATLAB implementation of the method, and illustrate our results with several examples and numerical experiments, including phase plots and plots of the basins of attraction.

Generalized Ostrowski root-finding method

1993 ◽  
Vol 57 (2-3) ◽  
pp. 275-287 ◽  
Author(s):  
Lj. Petković ◽  
M. Petković
Keyword(s):  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

An improvement to Ostrowski root-finding method

2006 ◽  
Vol 173 (1) ◽  
pp. 450-456 ◽  
Author(s):  
Miquel Grau ◽  
José Luis Díaz-Barrero
Keyword(s):  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

On a cubically convergent derivative-free root finding method

2007 ◽  
Vol 84 (4) ◽  
pp. 505-513 ◽  
Author(s):  
Miodrag S. Petković ◽  
Ljiljana D. Petković
Keyword(s):  
Root Finding ◽  
Derivative Free ◽  
Root Finding Method ◽  
Finding Method

A Root-Finding Method for Assessing SRAM Stability

2008 ◽  
Author(s):  
Rouwaida Kanj ◽  
Zhuo Li ◽  
Rajiv Joshi ◽  
Frank Liu ◽  
Sani Nassif
Keyword(s):  
Root Finding ◽  
Root Finding Method ◽  
Finding Method
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