Characterization Theorem for Best Polynomial Spline Approximation with Free Knots, Variable Degree and Fixed Tails

Least Squares Cubic Spline Approximation I Fixed Knots

Non-uniform spline recovery from small degree polynomial approximation

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds ...

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...

Good approximation by splines with variable knots

Here, t1, . . . , tN are the knots or joints of s ∈ S k π, and their multiplicity, i.e., equality among two or more of these, indicates reduced smoothness at that knot location in the usual way. Best approximation to f by elements of S π is quite well understood for a variety of norms since, after all, S π is a linear space. It seems practically more important and theoretically more interesting...

A Characterization Theorem for the Discrete Best Monotonic Approximation Problem

A characterization theorem is derived that motivates a procedure for generating discrete best monotonie approximations to n sequential data values, when a strictly convex objective function is used in the calculation. The procedure is highly useful in the discrete nonlinear optimization calculation that produces the best piecewise monotonie approximations to the data.