Divided Differences, Falling Factorials, and Discrete Splines

Ryan J. Tibshirani

doi:10.1561/2200000099

Divided Differences, Falling Factorials, and Discrete Splines

2022-01-01

3

OA

AI

R

Ryan J. Tibshirani *

DOI：10.1561/2200000099

原文链接

原文求助

摘要

En 中文

This monograph reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a suitable notion of) continuity in divided differences. As it happens, discrete splines bear connections to a wide array of developments in applied mathematics and statistics, from divided differences and Newton interpolation (dating back to over 300 years ago) to trend filtering (from the last 15 years). We survey these connections, and contribute some new perspectives and new results along the way.

Keyword:

TREND

LASSO

Divided Differences, Falling Factorials, and Discrete Splines

摘要

期刊

机构