# دانلود رایگان مقاله abscissae Greville از پایگاه های کاملا مثبت

عنوان فارسی
abscissae Greville از پایگاه های کاملا مثبت
عنوان انگلیسی
Greville abscissae of totally positive bases
صفحات مقاله فارسی
0
صفحات مقاله انگلیسی
15
سال انتشار
2016
نشریه
الزویر - Elsevier
فرمت مقاله انگلیسی
PDF
کد محصول
E543
رشته های مرتبط با این مقاله
مهندسی کامپیوتر و ریاضی
گرایش های مرتبط با این مقاله
نرم افزار و آنالیز عددی
مجله
طراحی هندسی به کمک کامپیوتر - Computer Aided Geometric Design
دانشگاه
دانشگاه د ساراگوسا، اسپانیا
کلمات کلیدی
abscissae Greville، طول حیاتی، مجموع مثبت
مقدمه

1. Introduction

Integral recurrence formulae for B-splines have been often used in the past. The definition of B-spline as a divided difference of a truncated power function and the Hermite–Gennochi formula lead to integral recursions. One of the first papers where it is observed that the sequence of B-spline bases can be obtained by successive integration in the general context of Chebyshevian splines is Bister and Prautzsch (1997). Bernstein polynomials as well as many other examples of totally positive bases in extended Chebyshev spaces are included in this setting. Totally positive bases (TP) are bases whose collocation matrices have nonnegative minors. This kind of bases are commonly used in computer-aided design due to their shape preserving properties (see Goodman, 1996). Among all normalized TP bases of a space, we can find normalized B-bases, which are the optimal shape preserving bases (cf. Carnicer and Peña, 1994). Spaces containing algebraic polynomials and trigonometric or hyperbolic functions have attracted much interest in the field of computer-aided geometric design (Zhang, 1996; Mainar et al., 2001). In Chen and Wang (2003), integral constructions of Bernstein-like basis for cycloidal spaces Cn = cos t, sint, 1,t,...,t n−2 have been provided. In Costantini et al. (2005), such constructions are discussed in a more general setting, showing that the integral constructions provide TP bases. In particular, the normalized B-basis is expressed using integrals of a B-basis of the space of derivatives. Greville abscissae are the coefficients of the function t with respect to a given basis and play a fundamental role in the definition of Bernstein-like operators in spaces of exponential polynomials (cf. Aldaz et al., 2009).

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