Tensor spline approximation

Tensor Product Spline Surface Approximation of a Discrete Point Field

1. Theoretical approach Designing the appropriate surface that approximates a certain point vector is one of the most challenging engineering tasks. Some of the aero and hydrodynamic profiles, materials plastic deformation technological problems are to be approached through surface approximation. Usually, the discrete input is achieved after coordinate measuring of a certain model. The designer...

Perfect spline approximation

Our study of perfect spline approximation reveals: (i) it is closely related to Σ∆ modulation used in one-bit quantization of bandlimited signals. In fact, they share the same recursive formulae, although in different contexts; (ii) the best rate of approximation by perfect splines of order r with equidistant knots of mesh size h is hr−1. This rate is optimal in the sense that a function can be...

Best Quadratic Spline Approximation

We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation. Higher-order simplicial elements can approximate data better than linear elements. Thus, fewer quadratic elements are required to achieve similar approximation quality. We use quadratic basis functions and compute best quadratic simplicial spline approxim...

Parallel Spline Approximation

Three-monotone spline approximation

For r ≥ 3, n ∈ N and each 3-monotone continuous function f on [a, b] (i.e., f is such that its third divided differences [x0, x1, x2, x3] f are nonnegative for all choices of distinct points x0, . . . , x3 in [a, b]), we construct a spline s of degree r and of minimal defect (i.e., s ∈ Cr−1[a, b]) with n −1 equidistant knots in (a, b), which is also 3-monotone and satisfies ‖ f − s‖L∞[a,b] ≤ cω...