rekurrensrelasjoner

A recurrence relation, or rekurrensrelasjon in Norwegian, is an equation that recursively defines a sequence, meaning that each term of the sequence is defined as a function of the preceding terms. In simpler terms, it's a rule that tells you how to get the next number in a sequence based on the numbers that came before it.

Common examples include the Fibonacci sequence, where each number is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8...). Another simple recurrence relation is an arithmetic progression, where a constant difference is added to each term to get the next.

Recurrence relations are fundamental in computer science, particularly in algorithm analysis. They are used to describe the running time of recursive algorithms. For instance, the time complexity of a divide-and-conquer algorithm might be expressed using a recurrence relation. Solving these relations helps determine the efficiency of an algorithm, often leading to Big O notation.

In mathematics, recurrence relations appear in various fields such as discrete mathematics, combinatorics, and number theory. They can be used to model population growth, compound interest, and many other phenomena that evolve over time in discrete steps.

The study of recurrence relations involves finding explicit formulas for the terms of the sequence, rather than just the recursive definition. This process, known as solving the recurrence relation, can be done using various techniques, including characteristic equations, generating functions, or iterative substitution.