Open AccessRepresentations of continuous piecewise affine functions
Author(s) -
Vassili N. Malozemov,
G. Sh. Tamasyan
Publication year - 2022
Publication title -
vestnik sankt-peterburgskogo universiteta. matematika. mehanika. astronomiâ/vestnik sankt-peterburgskogo universiteta. seriâ 1, matematika, mehanika, astronomiâ
Language(s) - English
Resource type - Journals
eISSN - 2587-5884
pISSN - 1025-3106
DOI - 10.21638/spbu01.2022.106
Subject(s) - piecewise , mathematics , affine transformation , affine hull , representation (politics) , polynomial , algebra over a field , pure mathematics , connection (principal bundle) , affine coordinate system , affine shape adaptation , affine combination , affine space , mathematical analysis , geometry , law , politics , political science
Continuous piecewise affine functions are widely used in computational mathematics. In one-dimensional case such functions are called broken lines. The article analyzes the analytical representations of broken lines in the forms accepted in the theory of polynomial splines as well as in the form of the difference of the maxima of two finite families of affine functions. The connection between these representation is being determined.