The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects ...

We prove that for a 3-monotone function F ∈ C[−1, 1], one can achieve the pointwise estimates |F(x) − Ψ(x)| ≤ cω3(F, ρn(x)), x ∈ [−1, 1], where ρn(x) := 1 n2 + √ 1−x2 n and c is an absolute constant, both with Ψ , a 3-monotone quadratic spline on the nth Chebyshev partition, and with Ψ , a 3-monotone polynomial of degree ≤ n. The basis for the construction of these splines and polynomials is th...

We give a new time-dependent definition of spline curves in Rn, which extends a recent definition of vector-valued splines introduced by Rodrigues and Silva Leite for the time-independent case. Previous results are based on a variational approach, with lengthy arguments, which do not cover the non-autonomous situation. We show that the previous results are a consequence of the Pontryagin maximu...

Tchebycheffian splines are smooth piecewise functions whose pieces drawn from (possibly different) Tchebycheff spaces, a natural generalization of algebraic polynomial spaces. They enjoy most the properties known in spline case. In particular, under suitable assumptions, admit representation terms basis functions, called B-splines (TB-splines), completely analogous to B-splines. A particularly ...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...