Numerical Analysis - Finding the Rate of Convergence

In summary, the conversation is about constructing a code in determining the Asymptotic Error Constant and the order of the rate of convergence for several iterative methods using Scilab 4.0. The person already knows the orders of the methods but needs help in determining the general code for ANY iteration. They mention a tutorial by Scilab professional partner, openeering, that may be helpful.
  • #1
relinquished™
79
0
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~
 
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  • #2
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.
 

1. What is Numerical Analysis?

Numerical Analysis is a branch of mathematics that deals with the development, analysis, and implementation of algorithms for solving problems involving continuous variables.

2. What is the Rate of Convergence?

The Rate of Convergence is a measure of how quickly a numerical method approaches the exact solution of a problem as the number of iterations increases.

3. How is the Rate of Convergence calculated?

The Rate of Convergence is calculated by taking the limit of the ratio of the error of a numerical method at two consecutive iterations to the error at the current iteration, as the number of iterations approaches infinity.

4. Why is the Rate of Convergence important?

The Rate of Convergence is important because it provides information about the efficiency and accuracy of a numerical method. A higher rate of convergence indicates a faster convergence to the solution, making the method more efficient.

5. How can the Rate of Convergence be improved?

The Rate of Convergence can be improved by using more efficient numerical methods or by optimizing the parameters of the existing method. It can also be improved by using a smaller step size in the iterative process.

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