caa a22 4500 467939209 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-7636-x doi (NATIONALLICENCE)springer-10.1007/s10444-004-7636-x On the generalized Ball bases [Elektronische Daten] [Jorge Delgado, Juan Peña] 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. Springer, 2006 shape preservation nationallicence evaluation algorithms nationallicence error analysis nationallicence total positivity nationallicence Delgado Jorge Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain aut Peña Juan Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 263-280 1019-7168 24:1-4<263 2006 24 10444 https://doi.org/10.1007/s10444-004-7636-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7636-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Delgado Jorge Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain aut NATIONALLICENCE 700 1- Peña Juan Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 263-280 1019-7168 24:1-4<263 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer