Perusratkaisu

Perusratkaisu, literally “basic solution” in Finnish, is a term used in mathematics, optimization and education to denote the fundamental or simplest method for solving a problem. In Finnish technical literature it frequently appears in the context of linear algebra and linear programming as the basic solution of a system or optimization problem.

Definition in linear programming: Consider Ax = b with x ≥ 0, where A is an m×n matrix. A set of m columns of A that are linearly independent is called a basis. The basic solution corresponding to that basis sets the nonbasic variables to zero and solves A_B x_B = b for x_B. If x_B ≥ 0, the result is a basic feasible solution; such a solution corresponds to a vertex of the feasible region and is a central concept in the simplex method, which moves from one basic feasible solution to another.

Beyond mathematics, perusratkaisu can also refer to a baseline or introductory solution in problem solving. It denotes the straightforward, well-established method used to obtain a result, often serving as a reference for evaluating more advanced or specialized approaches.

See also: basic solution, basic feasible solution, simplex method, linear programming, baseline solution.