totalvariationdiminishing
Total variation diminishing (TVD) is a mathematical property that describes the behavior of certain functions, particularly those that are monotonic or have a limited rate of change. A function is said to be total variation diminishing if the total variation of its output is less than or equal to the total variation of its input. This concept is particularly relevant in the fields of functional analysis, harmonic analysis, and the study of operators on function spaces.
The total variation of a function f on an interval [a, b] is defined as the supremum
TV(f) = sup { sum |f(xi) - f(xi-1)| : P is a partition of [a, b] }.
A function f is total variation diminishing if for any interval [a, b], the total variation of
Total variation diminishing functions are important in various applications, including signal processing, image analysis, and the