A cubic spline approximation in C1 to the solution of a general Volterra integral equation of the second kind is constructed. Under certain conditions, convergence of the approximation and its first two derivatives is proved and error bounds are obtained. The question of stability is not examined.

The basic idea of the Meir/Sharma/Hall/Meyer error analysis for cubic spline interpolation (see [SM66], [H68], [HM76]) has been extended to cover also certain deficient quartic and quintic spline interpolation schemes, the latter already by them, the former by Howell/Varma [HV89] and, perhaps, others. It is the purpose of this note to describe the most general situation to which this idea appli...

In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for approximation by linear combinations of nonuniform translates of the Sobolev splines. Our results extend previous work as we obtain rates for ba...

In this work, a computational method for solving nonlinear Volterra-Fredholm-Hammerestein integral equations is proposed. Compactly supported semiorthogonal cubic B-spline wavelets are employed as basis functions then collocation method is utilized to reduce the computation of integral equations to some algebraic system. The method is computationally attractive, and applications are demonstrate...

This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a diffe...

The paper discusses penalised spline (P -spline) smoothing for hazard regression of multivariable survival data. Non-proportional hazard functions are fitted in a numerically handy manner by employing Poisson regression which results from numerical integration of the cumulative hazard function. Multivariate smoothing parameters are selected by utilizing the connection between P -spline smoothin...

The original theory of splines grew out of the study of simple variational problems. A spline was a function that minimized some notion of energy subject to a set of interpolation constraints. A more recent method for creating splines is subdivision. A spline is the limit of a sequence of functions, each related by some simple averaging rule. This paper shows that the two ideas are intrinsicall...

Although edge detection is a well investigated topic, 3D edge detectors mostly lack either accuracy or speed. We will show, how to build a highly accurate subvoxel edge detector, which is fast enough for practical applications. In contrast to other approaches we use a spline interpolation in order to have an efficient approximation of the theoretically ideal sinc interpolator. We give theoretic...

A C curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The monotone rational cubic spline scheme has a unique representation.

The construction of classical hierarchical B–splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only decreases the overlapping of supports ...