Name
Abstract | ||
|---|---|---|
The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said–Ball and the Wang–Ball basis, respectively. In this paper, we analyze some shape preserving
and stability properties of these bases. We prove that the Wang–Ball basis is strictly monotonicity preserving for all m. However, it is not geometrically convexity preserving and is not totally positive for m>3, in contrast with the Said–Ball basis. We prove that the Said–Ball basis is better conditioned than the Wang–Ball basis
and we include a stable conversion between both generalized Ball bases. The Wang–Ball basis has an evaluation algorithm with
linear complexity. We perform an error analysis of the evaluation algorithms of both bases and compare them with other algorithms
for polynomial evaluation. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10444-004-7636-x | Adv. Comput. Math. |
Keywords | Field | DocType |
shape preservation,evaluation algorithms,error analysis,total positivity | Discrete mathematics,Mathematical optimization,Convexity,Polynomial,Generalization,Mathematical analysis,Cubic function,Basis function,Linear complexity,Monotonicity preserving,Mathematics | Journal |
Volume | Issue | ISSN |
24 | 1-4 | 1019-7168 |
Citations | PageRank | References |
4 | 0.69 | 16 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. Delgado | 1 | 107 | 17.39 |
| Juan Manuel Peña | 2 | 131 | 26.55 |