Polynomial degree reduction in the L-2-norm equals best Euclidean approximation of Bezier coefficients

Authors
Lutterkort, D Peters, J Reif, U
Citation
D. Lutterkort et al., Polynomial degree reduction in the L-2-norm equals best Euclidean approximation of Bezier coefficients, COMP AID G, 16(7), 1999, pp. 607-612
Citations number
6
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTER AIDED GEOMETRIC DESIGN
ISSN journal
01678396 → ACNP
Volume
16
Issue
7
Year of publication
1999
Pages
607 - 612
Database
ISI
SICI code
0167-8396(199908)16:7<607:PDRITL>2.0.ZU;2-S
Abstract
Given a polynomial p of degree n we want to find a best L-2-approximation o ver the unit interval from polynomials of degree m < n. This problem is sho wn to be equivalent to the problem of finding the best Euclidean approximat ion of the vector of Bernstein-Bezier coefficients of p from the vector of degree-raised Bernstein-Bezier coefficients of polynomials of degree m. (C) 1999 Elsevier Science B.V. All rights reserved.