convergence rates

Convergence rates describe how quickly an algorithm or method approaches its final, accurate result over time or iterations. Think of it like a car approaching a destination: a fast convergence means the car gets close to the destination quickly, while a slow rate indicates it takes longer. In mathematical terms, it measures how the error decreases as the process continues. Knowing the convergence rate helps us understand the efficiency of an algorithm—whether it reaches a good solution rapidly or requires many steps, guiding us in choosing the most appropriate method for the problem at hand.