===== Algorithm =====

An **algorithm** is a **step-by-step set of rules or instructions** designed to perform a specific task or solve a particular problem.

==== Key Characteristics ====
  * **Finite**: An algorithm must complete after a finite number of steps.
  * **Well-defined**: Each step must be clear and unambiguous.
  * **Deterministic** (in classical algorithms): The same input always produces the same output.
  * **Input**: Takes zero or more defined inputs.
  * **Output**: Produces at least one result.

==== Applications ====
  * **Computer Science**: Sorting, searching, data encryption, machine learning.
  * **Medicine**: Diagnostic workflows, image analysis, treatment decision trees.
  * **Mathematics**: Calculations, equation solving, number theory.
  * **Neuroscience**: Signal processing, tractography, pattern recognition.

==== Example ====
  * **Dijkstra's Algorithm**: Finds the shortest path between two points in a graph.
  * **UKF-2T Algorithm**: A tractography method for estimating complex neural fiber trajectories using Unscented Kalman Filters and two-tensor modeling.

==== Etymology ====
Derived from the name of Persian mathematician **al-Khwārizmī**, whose works introduced decimal positional number systems and systematic problem-solving methods to the Western world.

==== See Also ====
  * [[machine_learning]]
  * [[tractography]]
  * [[data_structure]]