functional analysis

functional analysis

Branch of mathematical analysis dealing with functionals, or functions of functions. It emerged as a distinct field in the 20th century, when it was realized that diverse mathematical processes, from arithmetic to calculus procedures, exhibit very similar properties. A functional, like a function, is a relationship between objects, but the objects may be numbers, vectors, or functions. Groupings of such objects are called spaces. Differentiation is an example of a functional because it defines a relationship between a function and another function (its derivative). Integration is also a functional. Functional analysis focuses on classes of functions, such as those that can be differentiated or integrated.

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functional analysis [¦′fəŋk·shən·əl ə′nal·ə·səs]

(mathematics)

A branch of analysis which studies the properties of mappings of classes of functions from one topological vector space to another.

(systems engineering)

A part of the design process that addresses the activities that a system, software, or organization must perform to achieve its desired outputs, that is, the transformations necessary to turn available inputs into the desired outputs.