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Optimal bases for a class of mixed spaces and their associated spline spaces

✍ Scribed by E. Mainar; J.M. Peña

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
985 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

We consider spaces of the form span 1, t, . . . , t n-4 , u 1 (t), u 2 (t), u 3 (t), u 4 (t) , where the functions u i (i = 1, . . . , 4) are algebraic polynomials, or trigonometric or hyperbolic functions. We find intervals [0, α] where we can guarantee that the spaces possess normalized totally positive bases (and so, shape preserving representations). We construct their normalized B-bases (with optimal shape preserving properties). We also present a unified approach to deal with the associated spline spaces. A recursive procedure to obtain bases with optimal shape preserving and stability properties is presented.

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