Kriteeriumjuurtest

Kriteeriumjuurtest is a term used in Estonian mathematical literature to refer to the subset of roots of an equation or function that satisfy a predefined set of criteria. This concept is used when not all mathematical roots are admissible for a given problem, and additional constraints determine which roots are considered valid or meaningful in a particular context. Kriteeriumjuurtest emphasizes the idea that solution sets may be filtered by external requirements beyond the equation itself.

A common approach is to specify a collection of criteria, such as reality (roots must be real), sign or magnitude constraints, location within a specified interval, or simplicity (roots with multiplicity one). Once the criteria are defined, root-finding methods are paired with post-processing filters to identify the kriteeriumjuurtest. Techniques include bracketing and interval methods, iterative methods with constraint checks, and interval analysis to guarantee that only admissible roots are reported.

Examples help illustrate the idea. Consider the polynomial p(x) = x^2 − 5, whose roots are −√5 and √5. Under the criterion x > 0, the kriteeriumjuurtest is {√5}. If the criterion is |x| < 3, the kriteeriumjuurtest is {−√5, √5}. Such selection is common in physics, engineering, and numerical analysis, where computed roots must comply with physical or design constraints rather than merely solving the equation.

See also: root finding, constrained optimization, interval analysis, polynomial equations, admissible solutions.