Name
Title | ||
|---|---|---|
Regularity and well-posedness of a dual program for convex best C1-spline interpolation |
Abstract | ||
|---|---|---|
An efficient approach to computing the convex best C 1-spline interpolant to a given set of data is to solve an associated dual program by standard numerical methods (e.g., Newton's method). We study regularity and well-posedness of the dual program: two important issues that have been not yet well-addressed in the literature. Our regularity results characterize the case when the generalized Hessian of the objective function is positive definite. We also give sufficient conditions for the coerciveness of the objective function. These results together specify conditions when the dual program is well-posed and hence justify why Newton's method is likely to be successful in practice. Examples are given to illustrate the obtained results. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s10589-007-9027-y | Comp. Opt. and Appl. |
Keywords | Field | DocType |
efficient approach,sufficient condition,convex best interpolation,splines,well-posedness,objective function,regularity result,1-spline interpolant,c1-spline interpolation,newton method,standard numerical method,dual program,important issue,degeneracy.,regularity,generalized hessian,positive definite,spline interpolation,degeneracy,numerical method | Spline (mathematics),Mathematical optimization,Spline interpolation,Mathematical analysis,Positive-definite matrix,Interpolation,Hessian matrix,Degeneracy (mathematics),Numerical analysis,Mathematics,Newton's method | Journal |
Volume | Issue | ISSN |
37 | 3 | 0926-6003 |
Citations | PageRank | References |
2 | 0.42 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Houduo Qi | 1 | 437 | 32.91 |
| Xiaoqi Yang | 2 | 126 | 20.85 |