Bounds for divided differences of grid function
- 1 January 1980
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 2 (2) , 219-230
- https://doi.org/10.1080/01630568008816054
Abstract
Let denote a family of nonuniform grids over [a,b], and (m!) DmyH be the m–th. divided difference of a grid function yH. Under the sole assumption that the grid is locally quasi uniform, i.e. , it is shown that there exists a spline function SH ε Cm[a,b] which interpolates a given grid function yH and satisfies for the inequalities with constants c0,c1 depending only m,p. Here ‖ ·‖p and ‖·‖H,P denotes a LP–norm and a discrete LP–norm, respectively. This inequality is a useful tool, for example, in handling compactness arguments for grid function or in proving discrete Sobolev inequalities on nonuniform grids.Keywords
This publication has 1 reference indexed in Scilit:
- How small can one make the derivatives of an interpolating function?Journal of Approximation Theory, 1975