Showing papers on "Monotone cubic interpolation published in 1973"
TL;DR: In this article, it was shown that the cardinal spline interpolation problem has a unique solution that grows like a power of |x| provided that all data grows like the Lagrange formula.
49 citations
TL;DR: In this paper, the authors gave explicit error bounds for bicubic spline interpolation and gave similar bounds for the cubic spline-blended interpolation scheme of Gordon.
37 citations
28 citations
TL;DR: In this paper, the authors investigated the B-splines for the case of Hermite interpolation (γ > 1) and derived an explicit solution for the problem (1), where v = 0, 1, n, n.
28 citations
27 citations
14 citations
14 citations
TL;DR: In this paper, a generalization of B-spline is used to improve the numerical behavior of the interpolation process. But this generalization is not suitable for a large class of spline interpolation problems.
Abstract: This paper generates interpolatingM-splines in the sense of Lucas [J. of Approx. Th. 5, 1---14 (1972)] by a simple algebraic construction. The method yieldsM-spline interpolants for every finite family of functionals commuting with the remainder term of a generalized Taylor formula. These assumptions are fulfilled for a large class of spline interpolation problems (e.g. splines generated by certain singular differential operators and splines of several variables) without any further requirements about the geometrical distribution or denseness of the interpolation points. A generalization ofB-splines is used to improve the numerical behaviour of the interpolation process.
12 citations
TL;DR: This part details the mathematical basis for the spline calculation used in the principal subroutine of the cubic spline package developed by the c.a.d. research group.
Abstract: Part 1 of this paper provided a user's guide to cubic spline package developed by the c.a.d. research group at Cambridge University Engineering Department. This part details the mathematical basis for the spline calculation used in the principal subroutine.
11 citations
TL;DR: In this paper, an algorithm for the Hermite-Birkhoff interpolation is presented, which reduces the problem to the problem of Hermite interpolation, and the missing values and derivatives are expressed by some of the given values and calculated from a system of linear equations.
Abstract: An algorithm for the Hermite-Birkhoff interpolation is presented, which reduces the problem to the Hermite interpolation. The missing values and derivatives are expressed by some of the given values and calculated from a system of linear equations. The system itself and its right-hand sides are computed from a set of Hermite interpolation problems. The needed values and derivatives of the Hermite interpolation polynomial can be computed using the algorithm given in the Appendix.
TL;DR: In this paper, the Slater-Koster interpolation method is used to find the explicit form of the matrix elements of the Hamiltonian between Bloch functions and so make possible the calculation of the energy bands in crystals with a cubic structure of perovskite type.
Abstract: The Slater-Koster interpolation method is used to find the explicit form of the matrix elements of the Hamiltonian between Bloch functions and so make possible the calculation of the energy bands in crystals with a cubic structure of perovskite type. In the nearest-neighbors approximation the energy matrix contains 23 independent parameters. The obtained formulas can be applied to a wide class of substances with the stated structure.
TL;DR: In this paper, the authors established the minimum norm property, the existence and uniqueness of a solution of the interpolation problem, the property of best approximation, and the convergence of interpolation processes.
Abstract: The choice of function space allows us to make conclusions in the multidimensional case that are analogous to results in the theory of spline functions of one variable. We establish the minimum norm property, the existence and uniqueness of a solution of the interpolation problem, the property of best approximation, and the convergence of interpolation processes.
TL;DR: The cubic spline approximation to the fourth-order differential equation y is shown to reduce to the solution of a five-term recurrence relationship.
Abstract: The cubic spline approximation to the fourth-order differential equation yiu + p(x)y″ + q(x)y′ + r(x)y = t(x) is shown to reduce to the solution of a five-term recurrence relationship. For some special cases the approximation is shown to be simply related to a finite difference representation with a local truncation error of order (1/720)d8y.