# cubic spline

## cubic spline

[′kyü·bik ′splīn]
(mathematics)
One of a collection of cubic polynomials used in interpolating a function whose value is specified at each of a collection of distinct ordered values, Xi (i =1, …, n), and whose slope is specified at X1 and Xn ; one cubic polynomial is found for each interval, such that the interpolating system has the prescribed values at each of the Xi, the prescribed slope at X1 and Xn, and a continuous slope at each of the Xi.
Mentioned in ?
References in periodicals archive ?
Several covariates were incorporated in the main GLM: a) a natural cubic spline smooth function of calendar day with 7 degrees of freedom (df) per year to exclude seasonality in mortality; b) a factor variable for "day of week" to exclude possible variations of mortality within a week; c) a cross-basis function of temperature built by the distributed lag nonlinear model (DLNM) to control for its potentially nonlinear and lagged confounding effects; and d) a natural smooth function with 3 df for the present-day relative humidity.
The exceptions from this category are the Cubic Spline filter with parameter [alpha]=-1 and the Box filter, which sometimes showed average performance, comparable to that of Flat-Top windowed-sinc, or worst performance, depending on the content of the image.
Inspired by the discovery that the shape of passenger vehicles is smooth and continuous within the surfaces defined by corresponding boundary lines, SMA provides three different spline options SMA: linear, cubic spline, and Piecewise Cubic Hermite Interpolation (PCHIP).
Buse and Lim (1977) agreed on Poirier's proposal and, by following him, they argued that cubic spline regression must be considered as a special form in restricted least squares.
f]), can be selected to obtain the reference trajectory by solving (11a), which is a cubic spline curve equation:
It is well known that the cubic spline function has advantages of good convergence, approximation, stability, and second-order smoothness.
The new constructed scheme was based on employing non-polynomial cubic spline method (NPCSM).
The article entitled The Term Structure of Interest Rates and its Impact on the Liability Adequacy Test for Insurance Companies in Brazil analyzes the results of the Liability Adequacy Test, deriving from the use of various construction models, such as the interpolation technique by cubic spline, Svensson's model (adopted by the regulator), and Vasicek's model.
Smoothers (and parameters in italics) used are lowess (weighted quadratic least-squares), f (span); Friedman super smoother (cross-validated running lines), span (span); cubic spline, spar (smoothing parameter), Savitzky-Golay (local polynomial regression), p, f (polynomial order, frame size); Kalman (state space model), none; running mean, wsize (window size); Whittaker (recursive penalized B-splines), [lambda] (spline parameter); and exponential moving average (EMA) (weighted recursive exponential smoothing), [alpha] (spline parameter).
In short summary, the linear (more formally, bilinear interpolation in the context of two-dimensional array data) involves a simple point-slope imputation of data at points intermediate to true observation; the cubic spline (more formally, bicubic spline) involves a summed, iterative approximation through fitting a third-order polynomial [12].
A cubic spline interpolation has been proposed to solve integral equations by Kumar and Sangal [14].
The aim of this study was to compare two different lactation curve models (Woodand cubic spline regression model in two knots: CSR1 and CSR2) and to find the best model that provided a good description of the first lactation curve of Jersey cattle herd.

Site: Follow: Share:
Open / Close