Name
Abstract | ||
|---|---|---|
We derive a formula for an n-th order divided difference of the inverse of a function. The formula has a simple and surprising structure: it is a sum over partitions of a convex polygon with n + 1 vertices. The formula provides a numerically stable method of computing divided differences of k-th roots. It also provides a new way of enumerating all partitions of a convex polygon of a certain type, i.e., with a specified number of triangles, quadrilaterals, and so on, which includes Catalan numbers as a special case. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1090/S0025-5718-08-02144-3 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
divided differences,inverse functions,polygon partitions | Combinatorics,Polygon covering,Convex polygon,Krein–Milman theorem,Convex set,Pick's theorem,Star-shaped polygon,Affine-regular polygon,Monotone polygon,Mathematics | Journal |
Volume | Issue | ISSN |
77 | 264 | 0025-5718 |
Citations | PageRank | References |
3 | 0.58 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael S. Floater | 1 | 1333 | 117.22 |
| Tom Lyche | 2 | 3 | 0.58 |