On quartic splines with application to quadratures

Abstract

--ZusammenfassungOn Quartic Splines with Application to Quadratures. This paper presents a formulation and a study of an interpolatory quartic spline which interpolates the first and second derivatives of a given function. This formulation can be applied, in particular, to quadratures. AMS Subject Classifications

Constrained Fourth Order Latent Differential Equation Reduces Parameter Estimation Bias for Damped Linear Oscillator Models

“…This case produces bias particularly in the estimation of the damping parameter in LDEs (McKee et al, 2018). In the use of interpolation splines, fourth order splines reduce what is called "overshoot" by the spline (e.g., El Tarazi & Sallam, 1987). It seems reasonable that the fourth order LDE would similarly reduce bias in the damping parameter when the time series is interrupted by phase resets.…”

Direct cubic spline with application to quadrature

“…Subtracting, if follows that Subtracting fj'+ I from both sides and expanding about X j -I using Taylor's expansion of order 2 with integral remainder, we get One can show that both factors preceding f ( 5 ' ( s ) in the above integrals are negative in the intervals considered. It follows then, by the mean value theorem for integrals, that ( j = 1,2, ..., N -1) (7) h 3 ( 5 ) ISY+l -f;+I…”

Optimal properties for deficient quartic splines of Marsden type

“…Error estimates for C 3 -smooth quartic splines and for quartic splines that on midpoints matches with the first derivative were established in [4], [5], [12], [18], [20] and [21]. In [20], Theorem 1 is generalized by replacing the position of midpoints to a general type of interior points of the form 3 4 ].…”