pöördsummafunktsioon

Pöördsummafunktsioon, also known as the inverse summation function or cumulative distribution function in some contexts, describes the relationship between a cumulative value and the original sequence of numbers that generated it. It essentially allows one to reverse the process of summation. If we have a sequence of numbers $x_1, x_2, x_3, \dots$ and a corresponding sequence of cumulative sums $S_1, S_2, S_3, \dots$ where $S_n = \sum_{i=1}^n x_i$, the pöördsummafunktsioon aims to recover the original $x_i$ from the $S_n$.

The fundamental operation of the pöördsummafunktsioon is subtraction. Given a cumulative sum $S_n$, the previous cumulative sum $S_{n-1}$ can be subtracted to obtain the individual element $x_n$. Therefore, for $n > 1$, the relationship is $x_n = S_n - S_{n-1}$. For the first element, $x_1$, it is simply equal to the first cumulative sum, $S_1$. This inverse relationship is crucial in various fields where data is accumulated over time or across categories, such as finance, statistics, and signal processing. Understanding this function allows for the retrieval of original data points from aggregated information.