The famous de Boor conjecture states that the condition of the polynomial B-spline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree. For highly nonuniform knot meshes, like geometric meshes, the conjecture is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral c...

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that...

We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.

Estimation of monotone functions has broad applications in statistics, engineering, and science. This paper addresses asymptotic behaviors of monotone penalized spline estimators using constrained dynamical optimization techniques. The underlying regression function is approximated by a B-spline of an arbitrary degree subject to the first-order difference penalty. The optimality conditions for ...

This paper is part of the general project of proof mining, developed by Kohlenbach. By ”proof mining” we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs. We present logical metatheorems for classes of spaces from functional analysis and hyperbolic geometry, like Gromov hyperbolic spaces, R-trees and uniformly ...

In the study of smoothing spline estimators, some convolution-kernellike properties of the Green’s function for an appropriate boundary value problem, depending on the design density, are needed. For the uniform density, the Green’s function can be computed more or less explicitly. Then, integral equation methods are brought to bear to establish the kernel-like properties of said Green’s functi...

Davis, P. J. Interpolation and approximation, Blaisdell New York 1969 Dikshit,H. P. and Rana, S. S. Cubic Interpolatory splines with non uniform Meshes J. Approx. Theory Vol 45, no4(1985) C. A. Hall and Meyer, W. W. ; Optimal error bounds for cubic spline Interpolation J. Approx. Theory, 58 (1989), 59-67. Kopotun K. A. : Univariate spline equivalence of moduli of smoothness and application . Ma...