Two chain rules for divided differences and Faà di Bruno’s formula

DOI10.1090/S0025-5718-06-01916-8zbMath1113.05011OpenAlexW1483261444MaRDI QIDQ3426026

Tom Lyche, Michael S. Floater

Publication date: 7 March 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01916-8

Mathematics Subject Classification ID

Partitions of sets (05A18) Combinatorial aspects of partitions of integers (05A17) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) One-variable calculus (26A06)

Related Items (15)

On a \(q\)-analogue of Faà di Bruno's determinant formula ⋮ Perturbations and operator trace functions ⋮ A chain rule for multivariate divided differences ⋮ The approximation order of four-point interpolatory curve subdivision ⋮ A unified approach to some recurrence sequences via Faà di Bruno's formula ⋮ Trace formulas for resolvent comparable operators ⋮ Orthogonal projections and uniformly bounded families of multipliers ⋮ Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement ⋮ Some extensions of Faà di Bruno's formula with divided differences ⋮ Divided differences of inverse functions and partitions of a convex polygon ⋮ Some identities involving exponential functions and Stirling numbers and applications ⋮ On the Hermite interpolation ⋮ Divided differences of implicit functions ⋮ ASYMPTOTIC TIME DECAY IN QUANTUM PHYSICS: A SELECTIVE REVIEW AND SOME NEW RESULTS ⋮ General approach to constructing optimal multipoint families of iterative methods using Hermite's rational interpolation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Properties of \(\beta\)-splines
• Piecewise polynomial spaces and geometric continuity of curves
• Arc length estimation and the convergence of polynomial curve interpolation
• The Formula of FAA Di Bruno
• The Curious History of Faa di Bruno's Formula
• A general framework for high-accuracy parametric interpolation
• Derivatives of composite functions

This page was built for publication: Two chain rules for divided differences and Faà di Bruno’s formula