scholarly journals One-step iterative methods and their qualitative analysis

2006 ◽  
Vol 7 (1) ◽  
pp. 43
Author(s):  
Miklós Mincsovics
Keyword(s):  
Qualitative Analysis ◽  
Iterative Methods ◽  
One Step

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

Comparing the Energy of Convergence of One-Step and Two-Step Iterative Methods

2017 ◽  
Vol 53 (1) ◽  
pp. 21-25
Author(s):  
V. G. Prikazchikov ◽  
A. N. Khimich
Keyword(s):  
Iterative Methods ◽  
One Step

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation – Numerical Validation

2018 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ;  λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

On the Identification of Machine Settings for Gear Surface Topography Corrections

2011 ◽  
Author(s):  
Marco Gabiccini ◽  
Alessio Artoni ◽  
Massimo Guiggiani
Keyword(s):  
Iterative Methods ◽  
Gear Tooth ◽  
Nonlinear Least Squares ◽  
Tooth Surface ◽  
Generation Process ◽  
Sensitivity Matrix ◽  
One Step ◽  
Reliability And Robustness ◽  
Step Control

In this paper we set out to investigate the performances of some of the algorithms proposed in the gear literature for identifying the machine-settings required to obtain predesigned gear tooth surface topographies, or needed to compensate for flank form deviations of real teeth. For the ease of comparison, the problem is formulated as a nonlinear least-squares minimization, and the most widely employed algorithms are derived as particular cases. The algorithms included in the analysis are: (i) one-step methods; (ii) iterative methods; (iii) iterative methods with step control. The performance index is devised in their ability of returning practical solutions in the presence of: (i) strong model nonlinearities, (ii) ill-conditioning of the sensitivity matrix, (iii) demanding topographic shapes purposely selected. Instrumental here is an original classification of topographic modifications as either “simple” or “complex”, based on the SVD analysis of the sensitivity matrix. On the basis of the numerical tests documented, iterative techniques with step control seem the most convenient, due to reliability and robustness of the solutions produced. The generation process here considered is face-milling of hypoid gears, even though the methodology is general enough to cope with any gear cutting method requiring only some minor technical changes.

An Interactive Minicomputer Program for the Indexing and Simulation of Electron Diffraction Patterns

1976 ◽  
Vol 34 ◽  
pp. 542-543
Author(s):  
R.P. Goehner ◽  
W.T. Hatfield ◽  
Prakash Rao
Keyword(s):  
Electron Diffraction ◽  
Real Time ◽  
Pattern Analysis ◽  
Flow Diagram ◽  
Hard Copy ◽  
Time Analysis ◽  
Real Time Analysis ◽  
Transmission Electron ◽  
One Step ◽  
Diffraction Patterns

Computer programs are now available in various laboratories for the indexing and simulation of transmission electron diffraction patterns. Although these programs address themselves to the solution of various aspects of the indexing and simulation process, the ultimate goal is to perform real time diffraction pattern analysis directly off of the imaging screen of the transmission electron microscope. The program to be described in this paper represents one step prior to real time analysis. It involves the combination of two programs, described in an earlier paper(l), into a single program for use on an interactive basis with a minicomputer. In our case, the minicomputer is an INTERDATA 70 equipped with a Tektronix 4010-1 graphical display terminal and hard copy unit.A simplified flow diagram of the combined program, written in Fortran IV, is shown in Figure 1. It consists of two programs INDEX and TEDP which index and simulate electron diffraction patterns respectively. The user has the option of choosing either the indexing or simulating aspects of the combined program.

Nutrient-regulated gene expression in eukaryotes

2006 ◽  
Vol 73 ◽  
pp. 85-96 ◽  
Author(s):  
Richard J. Reece ◽  
Laila Beynon ◽  
Stacey Holden ◽  
Amanda D. Hughes ◽  
Karine Rébora ◽  
...  
Keyword(s):  
Gene Expression ◽  
Rna Polymerase ◽  
Rna Polymerase Ii ◽  
Transcriptional Control ◽  
Direct Interaction ◽  
Signalling Pathways ◽  
A Cell ◽  
One Step ◽  
Higher Eukaryotes ◽  
Regulated Gene Expression

The recognition of changes in environmental conditions, and the ability to adapt to these changes, is essential for the viability of cells. There are numerous well characterized systems by which the presence or absence of an individual metabolite may be recognized by a cell. However, the recognition of a metabolite is just one step in a process that often results in changes in the expression of whole sets of genes required to respond to that metabolite. In higher eukaryotes, the signalling pathway between metabolite recognition and transcriptional control can be complex. Recent evidence from the relatively simple eukaryote yeast suggests that complex signalling pathways may be circumvented through the direct interaction between individual metabolites and regulators of RNA polymerase II-mediated transcription. Biochemical and structural analyses are beginning to unravel these elegant genetic control elements.

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