منابع مشابه
A Geometric Proof of Total Positivity for Spline Interpolation
Simple geometric proofs are given for the total positivity of the B-spline collocation matrix and the variation diminishing property of the B-spline representation of a spline.
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We show that a refinable function φ with dilationM ≥ 2 is a ripplet, i.e., the collocation matrices of its shifts are totally positive, provided that the symbol p of its refinement mask satisfies certain conditions. The main condition is that p (of degree n) satisfies what we term condition (I), which requires that n determinants of the coefficients of p are positive and generalises the conditi...
متن کاملRegulators and Total Positivity
The classical regulator R of a number field K is given [F1] by a rapidly convergent series of the form R w = ∞
متن کاملTotal Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument
In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0F1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0F1 functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arb...
متن کاملTotal Positivity and Convexity Preservation
It is well established that systems of totally positive blending functions, such as the Bernstein and B-spline bases, preserve monotonicity and convexity and are generally ‘shape preserving’ [9 ]. In this paper we show that total positivity is equivalent to the preservation of all orders of convexity. By a system we understand a sequence of functions (u0, . . . , un) defined on an interval [a, ...
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ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 1996
ISSN: 1988-2807,1139-1138
DOI: 10.5209/rev_rema.1996.v9.17539