TY - JOUR

T1 - Representations of Continuous Piecewise Affine Functions

AU - Malozemov, V. N.

AU - Tamasyan, G. Sh

N1 - Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/3

Y1 - 2022/3

N2 - Abstract: Continuous piecewise affine functions are widely used in computational mathematics. In the one-dimensional case, such functions are called broken lines. The paper analyzes the analytical representations of broken lines both in the forms accepted in the theory of polynomial splines and in the form of the difference of the maxima of two finite families of affine functions. We establish a correlation between these representations.

AB - Abstract: Continuous piecewise affine functions are widely used in computational mathematics. In the one-dimensional case, such functions are called broken lines. The paper analyzes the analytical representations of broken lines both in the forms accepted in the theory of polynomial splines and in the form of the difference of the maxima of two finite families of affine functions. We establish a correlation between these representations.

KW - analytical representations of broken lines

KW - broken line

KW - difference of convex functions

KW - piecewise affine function

UR - http://www.scopus.com/inward/record.url?scp=85131358155&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f55a915c-94ea-3ea1-801e-21ee99cc78ab/

U2 - 10.1134/S1063454122010083

DO - 10.1134/S1063454122010083

M3 - Article

AN - SCOPUS:85131358155

VL - 55

SP - 39

EP - 47

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -