Numerical Analysis - Finding the Rate of Convergence

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SUMMARY

This discussion focuses on determining the Asymptotic Error Constant and the order of the rate of convergence (r) for iterative methods such as Fixed Point, Newton-Raphson, and Secant methods using Scilab 6.0.2. The user seeks assistance in constructing a general code to calculate the asymptotic error constant applicable to any iteration. Relevant tutorials from Openeering, a Scilab professional partner, provide additional guidance on this topic.

PREREQUISITES
  • Understanding of iterative methods: Fixed Point, Newton-Raphson, and Secant methods
  • Familiarity with Scilab 6.0.2 programming environment
  • Knowledge of numerical analysis concepts, specifically convergence and error analysis
  • Basic coding skills to implement algorithms in Scilab
NEXT STEPS
  • Explore the Openeering tutorials on Scilab for iterative methods
  • Learn how to implement error analysis in Scilab
  • Research the mathematical foundations of asymptotic error constants
  • Investigate advanced features of Scilab for numerical computations
USEFUL FOR

Students and professionals in numerical analysis, software developers working with Scilab, and anyone interested in improving their understanding of iterative methods and convergence rates.

relinquished™
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Hello,

I'm trying to construct a code in determining the Asymptotic Error Constant and the order of the rate of convergence, r for several iterative methods like the Fixed point, Newton Rhapson, and Secant methods in determining roots, using Scilab 4.0 (which is said to behave much like MathLab, but I'm not that sure). I already know what their orders are, I just have a problem in determining the general code in determining the asymptotic error constant for ANY iteration. Any help is appreciated.

reli~
 
Technology news on Phys.org
Scilab is currently in version ##6.0.2##. As of now, there is this tutorial by openeering - a scilab professional partner, which is quite relevant to what is asked in the OP. Also, there are two more (relevant) tutorials besides the one already mentioned - all three posted on January 14, 2015, at openeering, here.
 

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