Showing papers on "Monotone cubic interpolation published in 1984"
TL;DR: In this paper, a method for producing monotone piecewise cubic interpolants to monotonous data is described, which is completely local and which is extremely simple to implement.
Abstract: A method is described for producing monotone piecewise cubic interpolants to monotone data which is completely local and which is extremely simple to implement.
294 citations
TL;DR: In this article, the authors adapt to the spherical case the basic theory and the computational method known from surface spline interpolation in Euclidean spaces, which is made simple and efficient for numerical computation.
72 citations
TL;DR: In this paper, a new approach to the problem of parametrizing data in parametric cubic spline interpolation problems is discussed, in part evidenced by reduced position overshoots and lower second derivatives.
56 citations
01 Jan 1984
TL;DR: One of the most efficient methods to date for global interpolation of scattered data has come to be called surface spline interpolation as discussed by the authors, which can be computed in closed form and is known in a functional semi-Hilbert space.
Abstract: One of the most efficient methods to date for global interpolation of scattered data has come to be called “surface spline interpolation”. It turns out that the underlying mathematical theory has for natural setting some functional semi-Hilbert space whose reproducing kernel is known in closed form and can be computed economically. Solving the interpolation problem thus amounts to minimizing some Sobolev seminorm under interpolatory constraints or eventually, to solving a positive definite linear system. Our purpose here is to give a motivated and self-contained presentation of this interesting material.
49 citations
TL;DR: In this article, a necessary and sufficient condition for the existence of cubic differentiable interpolating splines which are monotone and convex is presented, and their approximation properties when applied to the interpolation of functions having a preassigned degree of smoothness.
Abstract: Given a set of monotone and convex data, we present a necessary and sufficient condition for the existence of cubic differentiable interpolating splines which are monotone and convex. Further, we discuss their approximation properties when applied to the interpolation of functions having preassigned degree of smoothness.
40 citations
TL;DR: In this paper, a numerical method for solving the renewal equation is proposed, which generates a cubic spline approximation of the renewal function by the Galerkin technique, tested on Gamma lifetime densities of various shapes.
Abstract: A numerical method for solving the renewal equation is proposed. The method which generates a cubic spline approximation of the renewal function by the Galerkin technique is tested on Gamma lifetime densities of various shapes. Results are compared against known analytical solutions and earlier approximation.
32 citations
TL;DR: An algorithm for the construction of shape-preserving cubic splines interpolating a set of data point based upon some existence properties recently developed is presented.
Abstract: We present an algorithm for the construction of shape-preserving cubic splines interpolating a set of data point. The method is based upon some existence properties recently developed. Graphical examples are given.
23 citations
TL;DR: In this article, a variational approximation applicable to three-dimensional isotropic cubic lattice models is formulated, which correctly gives the first 14, 19, and 23 terms of the known low-temperature free energy expansion.
Abstract: A variational approximation applicable to three-dimensional isotropic cubic lattice models is formulated. When applied to the simple cubic, face centred cubic and body centred cubic Ising models, the approximation correctly gives the first 14, 19, and 23 terms respectively of the known low-temperature free energy expansion.
14 citations
01 Jan 1984
TL;DR: In this article, a rational cubic function is presented which has shape preserving interpolation properties and can be used to construct C 2 rational spline interpolants to monotonic or convex sets of data which are defined on a partition x 1 < x2 < … < xn of the real interval [x 1, xn].
Abstract: A rational cubic function is presented which has shape preserving interpolation properties. It is shown that the rational cubic can be used to construct C2 rational spline interpolants to monotonic or convex sets of data which are defined on a partition x1 < x2 < … < xn of the real interval [x1, xn].
14 citations
TL;DR: Cubic spline least squares fitting algorithms for continous functions and functions with jump discontinuities were developed for X-ray photoelectric cross sections in this paper, and the cubic spline coefficients for incoherent and coherent scattering cross sections for elements from sodium through cobalt were reported for energies from 1 to 150 keV, and when two interior knots (three regions) are used they yield accuracies better than those obtined by a single cubic polynomial.
10 citations
TL;DR: In this paper, a solution for the first non-trivial case of cubic interpolation is presented for the problem of explicitly determining a set of nodes which is optimal in the sense that it loads to minimal Lebesgue constants.
Abstract: A famous unsolved problem in the theory of polynomial interpolation is that of explicitly determining a set of nodes which is optimal in the sense that it loads to minimal Lebesgue constants. A solution to this problem is presented for the first non‐trivial case of cubic interpolation. This example has proved to be very instructive in numerical analysis courses.
TL;DR: In this article, a test of the accuracy of the linear interpolation used in the analytical tetrahedron method has been carried out with two different dispersion relations, and it was found that although the interpolation is suitable for spectral functions, it is not reliable for quantitative study of the Fermi wavevectors and Fermian surface cross sections.
01 Sep 1984
TL;DR: In this paper, a non-linear thick composite shell theory is presented in which the through-the-thickness displacements are modeled using a variation of a cubic spline.
Abstract: : A non-linear thick composite shell theory is presented in which the through-the-thickness displacements are modeled using a variation of a cubic spline. The theory is developed by considering the Lagrangian strains in conjunction with the 2nd Piola-Kirchhoff stress. This formulation leads to a theory which encompasses large displacements with moderately large rotations but is restricted to small strains. The imposition of the cubic distribution through-the-thickness insures that the compatibility of the displacements and their first and second derivatives and thus the shear strains are maintained from lamina to lamina. The cubic distribution is seen as a higher order approximation than has been previously employed, but because of the nature of the spline, the theory is less cumbersome and more easily implemented than the parabolic theory. In addition, there is no introduction of additional degrees of freedom with the cubic theory. A family of 2-D isoparametric elements is employed in conjunction with the theory to solve a class of 3-D thick plate problems. Results are presented showing comparisons which are in good agreement with previous work. Additional keywords: Finite element analysis; Composite materials; Laminates; Cubic spline technique; and Nonlinear analysis. (Author)
TL;DR: Some variational properties of (2, 0) and (3, 1) spline interpolations and their error estimates are considered in this article, where the error estimates of splines and splines are compared.
TL;DR: In this article, the authors studied the susceptibility critical amplitude for the classical n-vector model in the high-temperature expansion and showed the smooth and monotonic n-dependence of the amplitude for simple cubic, the body-centered cubic and the facecentered cubic lattices.
Abstract: We have studied the susceptibility critical amplitude \(\varGamma \) for the classical n -vector model in the high-temperature expansion. With the help of the Pade approximant, we have shown the smooth and monotonic n -dependence of the amplitude for the simple cubic, the body-centered cubic and the face-centered cubic lattices. The results are compared with the exact results for n = ∞.
TL;DR: In this paper, the convergence of quadratic spline interpolation is studied where the points of interpolation are kept uniformly away from the mesh points, and variational properties and convergence are studied.
TL;DR: In this article, algebraic conditions for interpolating piecewise cubic splines over two triangular elements with a common edge are found, and two methods of extending such cubic spline interpolates to arbitrary triangulations are introduced.
Abstract: Algebraic conditions which permit one to interpolate twice continuously differentiable piecewise cubic splines over two triangular elements with a common edge are found. Two methods of extending such cubic spline interpolates to arbitrary triangulations are introduced. Such extensions cannot as we see take place in an arbitrary manner and depend on the particular triangulation under consideration. An advantage to such cubic splines is that one can minimize strain energy in certain controlled directions.
TL;DR: In this article, it is shown that the cubic spline integration can be formulated in terms of quadrature weights, such that the determination of wt requires prior knowledge of the mesh points only.
Abstract: In computational physics it is often required to evaluate several different integrals on the same mesh of points which are arbitrarily spaced. If the standard method of cubic spline integration is used, then for each integral a new set of second derivatives of the cubic spline interpolant must be calculated. It is shown that the cubic spline integration can be formulated in terms of quadrature weights wi, i.e., ? f (x) dx ˜ ?iwifi, such that the determination of wt requires prior knowledge of the mesh points only. Hence the quadrature weights are independent of the integrand. Furthermore, if the integrand can be expressed as a product of a slowly varying function and an elementary, rapidly varying function, the latter can be incorporated into the quadrature weights so that only the slowly varying function is approximated by cubic spline. This procedure results in greatly improved accuracy in the numerical integration. This method of generating quadrature weights in cubic spline integration would also make...
01 Jan 1984
TL;DR: In this paper, a technique using least square cubic splines was developed to obtain an estimate of the MTF from edge response measurements by making specific assumptions concerning the general nature of edges to be analyzed.
Abstract: A technique using least square cubic splines was developed to obtain an estimate of the MTF from edge response measurements. By making specific assumptions concerning the general nature of edges to be analyzed, an optimized procedure was developed to fit noise free cummulative gaussian edges. The procedure was evaluated using simulated data from various spread function shapes and levels of additive noise. The spline technique produced MTF estimates which had less bias and lower variance than the commonly used derivative transform technique. Due to the various constraints which can be imposed on the spline, least square cubic splines actually comprise a class ofedge analysis techniques which spans the range of characteristics from the derivative transform technique to the exact functional form fitting technique. Because of the nature of the spline calculation, the constrained, least square cubic spline can be thought of as a matched, yet adaptive nonlinear filter.
01 Jan 1984
TL;DR: In this paper, the convergence property of cubic Bessel interpolation is investigated and an exact error evaluation for functions of continuous third derivative when the interpolation points are uniformly spaced is given.
Abstract: The convergence property of cubic Bessel interpolation is investigated and an exact error evaluation for functions of continuous third derivative when the interpolation points are uniformly spaced is given