Convergence Rate for Numerical Methods: Conditions and Positivity

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The convergence rate of a numerical method indicates how quickly a solution approaches the true value. A positive convergence rate is necessary for the method to be effective, as a zero or negative rate suggests that the solution is either stagnant or diverging. Conditions for convergence often include that the rate must be less than one to ensure improvement. Understanding the definition of convergence rate is crucial for evaluating the effectiveness of numerical methods. Overall, a positive convergence rate is essential for achieving reliable results in numerical analysis.
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Homework Statement



If we find the convergence rate of a numerical method, does this rate have to be positive? and are there any conditions eg rate must be less than 1?

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The Attempt at a Solution



Thank you
 
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what do you think?

zero or negative convergence rate would imply that the solution is not improving or actually diverging to me.

it may help to define exactly what the convergnce rate actually is
 

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