The appropriateness of various numerical procedures for obtaining valid time-derivative data recently reported in the literature (Zernicke et a/., 1976: McLaughlin er al., 1977; Pezzack et u/., 1977) is discussed. A case for the use of quintic natural splines is presented. based on the smoothness of higher derivatives and flexibility in application. \‘ES; /\ . _J”P JGTc, SE=5 :;yz,s’sy = z7 ___...

We first review B-splines and splines constructed using B-splines as the basis functions.

SUMMARY: Structural equation models are well-developed statistical tools for multivariate data with latent variables. Recently, much attention has been given to developing structural equation models that account for nonlinear relationships between the endogenous latent variables, the covariates, and the exogenous latent variables. [Guo et al. (2012)], developed a semiparametric structural equat...

A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...

For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...