Endurtekningarlausn

Endurtekningarlausn is an Icelandic term used in mathematics and computer science to describe a solution to a problem that does not rely on recurrence or repetition. The word is formed from elements meaning repetition and solution, conveying the idea of achieving a result without iterative repetition.

In mathematics, such solutions are often closed-form expressions or explicit constructions that satisfy the problem without solving a recurrence relation. They are common when a problem admits a direct formula for the quantity of interest, such as the sum of the first n natural numbers or the nth term of a geometric series. A non-recurrent solution provides a single formula or construction rather than a step-by-step iteration.

In computer science, endurtekningarlausn refers to non-recursive algorithms or implementations that avoid function self-calls and repeated work. Non-recursive solutions can be more space-efficient and sometimes faster on large inputs. For example, computing factorial n with a loop rather than by recursive calls, or using an iterative approach to the Fibonacci sequence instead of a naive recursive one.

Limitations exist: not all problems have a non-recurrent form, and a closed-form or explicit solution may not exist or may be impractical to derive. In some cases, recursive or dynamic programming approaches offer clearer reasoning, easier maintenance, or better numerical stability, even if they involve repetition or overlapping subproblems.

See also: closed form, recurrence relation, iterative algorithm, dynamic programming, explicit formula.