The formula to calculate the rate of convergence (ROC) is:
\[ ROC = \left| \frac{x_{n+1} - x_n}{x_n - x_{n-1}} \right| \]
Where:
The rate of convergence refers to the speed at which a sequence of numbers approaches a certain value or limit. It is a concept used in numerical analysis and is particularly important in the field of computational mathematics. The rate of convergence helps to determine how many iterations are needed to achieve a certain level of accuracy, and thus can be used to assess the efficiency of numerical methods. Different methods may have different rates of convergence, with faster rates being more desirable as they require fewer iterations to reach the desired precision.
Let's assume the following values:
Step 1: Calculate the Rate of Convergence (ROC):
\[ ROC = \left| \frac{1.5 - 1.3}{1.3 - 1.2} \right| = \left| \frac{0.2}{0.1} \right| = 2 \]
The rate of convergence is 2.
