Piecewise linear Guide, Meaning , Facts, Information and Description
A piecewise linear function , where V is a vector space and is a subset of a vector space, is any function with the property that can be decomposed into finitely many convex polytopes, such that f is equal to a linear function on each of these polytopes.
A special case is when f is a real-valued function on an interval . Then f is piecewise linear if and only if can be partitioned into finitely many sub-intervals, such that on each such sub-interval I, f is equal to a linear function f(x) = a_I x + b_I.
The absolute value function is a good example of a piecewise linear function. Other examples include the square wave, the sawtooth function, and the floor function.
Important sub-classes of piecewise linear functions include the continuous piecewise linear functions and the convex piecewise linear functions.