Paper Info
Title
Sharpness In Trajectory Estimation For Planar Four-Points Piecewise-Quadratic Interpolation
Abstract
This paper discusses the problem of fitting non-parametric planar data Q(m) = {q(i)}(i-0)(m) with four-points piecewise-quadratic interpolant to estimate an unknown convex curve gamma in Euclidean space E-2 sampled more-or-less uniformly. The derivation of the interpolant involves non-trivial algebraic and symbolic computations. As it turns out, exclusive symbolic computations with Wolfram Mathematica 9 are unable to explicitly construct the interpolant in question. The alternative solution involves human and computer interaction. The theoretical asymptotic analysis concerning this interpolation scheme as already demonstrated yields quartic orders of convergence for trajectory estimation. This paper verifies in affirmative the sharpness of the above asymptotics via numerical tests and independently via analytic proof based on symbolic computations. Finally, we prove the necessity of admitting more-or-less uniformity and strict convexity to attain at least quartic order of convergence for trajectory approximation. In case of violating strict convexity of gamma we propose a corrected interpolant (Q) over bar which preserves quartic order of convergence.
Year
DOI
Venue
2014
10.1007/978-3-319-10515-4_20
COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 2014
Field
DocType
Volume
Applied mathematics,Convexity,Mathematical analysis,Computer science,Interpolation,Symbolic computation,Rate of convergence,Artificial intelligence,Computer vision,Euclidean space,Quartic function,Convex curve,Bilinear interpolation
Conference
8660
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
4
3
Name
Order
Citations
PageRank
Ryszard Kozera116326.54
Lyle Noakes214922.67
Piotr Szmielew341.27