论文标题
分开的差异，下降阶乘和离散的花纹：另一个查看趋势过滤和相关问题
Divided Differences, Falling Factorials, and Discrete Splines: Another Look at Trend Filtering and Related Problems
论文作者
论文摘要
本文回顾了一类单变量分段多项式函数，称为离散花纹，它们具有类似于知名类样条函数的属性，但是衍生物中的连续性被分裂差异的连续性（适当的）连续性所取代。碰巧的是，离散的花纹与应用数学和统计数据的广泛发展相关，从分裂的差异和牛顿插值（可追溯到300年前）到趋势过滤（从过去的15年开始）。我们调查这些联系，并在此过程中贡献一些新的观点和新的结果。
This paper 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.
