Curve and surface fitting with splines

By P. Dierckx. 1996

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Multivariate calibration with temperature interaction using two-dimensional penalized signal regression (2003, unknown): “[11] (chapters 1 and 2).”
Free‐knot polynomial splines with confidence intervals (2003, background): “The truncated basis has a simple form and is easy to understand, but it is less stable computationally (Dierckx, 1993).”
A spatio-temporal Volterra modeling approach for a class of distributed industrial processes (2009, methodology): “Then one can use the curve/surface fitting method [31,20] interpolate the eigenfunctions to locations where the data are not available.”
Chaotic lensing around boson stars and Kerr black holes with scalar hair (2016, methodology): “bles are obtained by taking derivatives of the interpolant. The interpolation is performed using the RectBivariateSpline functionality of SciPy, which is based on the FITPACK implementation in Netlib [98]. The resulting values are then inserted in the analytical expressions for the actual metric com”
THE CARNEGIE SUPERNOVA PROJECT: ANALYSIS OF THE FIRST SAMPLE OF LOW-REDSHIFT TYPE-Ia SUPERNOVAE (2009, methodology): “We use the FITPACK library (Dierckx 1993), which employs a variable number of knots depending on the sampling and precision of the data.”
Spectrum radial velocity analyser (SERVAL). High-precision radial velocities and two alternative spectral indicators (2017, methodology): “Equation (16) is a linear least-squares problem due to the linearity of the coefficients in the B-spline (de Boor 1978; Dierckx 1993; Eilers & Marx 1996) used to describe the template F(x, b) = ∑ bkBk(x), (17) where B are the basic functions.”
Selection of smoothing parameters inB-spline nonparametric regression models using information criteria (2003, methodology): “For B-splines we refer to de Boor (1978), Dierckx (1993) and Eilers and Marx (1996).”
Direct generalized additive modeling with penalized likelihood (1998, background): “The basic B-spline reference is de Boor (1978), and we find Dierckx (1993) to have a nice presentation.”
An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation (2003, methodology): “2 See [ 23 ] for a detail exposition of the two classes of surface fitting problem.”
Analytical redundancy relations for fault detection and isolation in algebraic dynamic systems (2001, unknown): “Speci"c algorithms are extensively reported in the literature (Fox & Parker, 1968; David, 1975; Dierckx, 1993).”
Oblivious Neural Network Predictions via MiniONN Transformations (2017, methodology): “(4) Fit a smoothing spline ([22], Chapter 5) of the same order using the knots {αi } on the dataset {αi ,βi } and extract the polynomial expression Pi (α ) in the each interval [α̇i , α̇i+1],i ∈ {1,m − 1}.”
Electricity consumption prediction with functional linear regression using spline estimators (2010, background): “Hence, the estimator is a bivariate spline with a tensor product representation [7].”
SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python (2019, methodology): “…while benefiting from their performance: QUADPACK 51 and ODEPACK 52 for numerical integration and solution of initial value problems; FITPACK 53 , ODRPACK 54 and MINPACK 55 for curve-fitting and least-squares minimization; FFTPACK 56,57 for performing Fourier transforms; ARPACK 58 for…”
Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada (2002, unknown): “This discussion is a distillation of the results so aptly presented in Lancaster and Salkauskas (1986), Dierckx (1993), deBoor (1978), Ralston and Rabinowitz (1978), Press et al. (1992), and Anderson et al. (1996).”