Overlapping Additive Schwarz (OAS) preconditioners are here constructed for isogeometric collocation discretizations of the system linear elasticity in both two and three space dimensions. Isogeometric methods recent variants analysis based on numerical approximation strong form partial differential equations at appropriate points. Numerical results dimensions show that two-level OAS scalable n...

In this paper we report on the use of B-Spline lters in perfect reconstruction lter banks. For each polynomial order the analysis and synthesis FIR lters are evaluated, considering the error introduced by lter coe cient truncation, coding quantization and the distortion introduced by the lters themselves. It is shown that B-Spline lters exhibit higher energy concentration in the lower frequency...

This article was supposed to be on `multivariate splines'. An informal survey, taken recently by asking various people in Approximation Theory what they consider to be a `multivariate spline', resulted in the answer that a multivariate spline is a possibly smooth, piecewise polynomial function of several arguments. In particular, the potentially very useful thin-plate spline was thought to belo...

Deboor, C. , A Practical Guide to splines, Applied Mathematical Science, Vol. 27 Springer Verlag, New York, 1979. Hall, C. A. and Meyer, W. W. , J. Approximation Theory, 16(1976), pp. 105-122. Howel, G. and Verma, A. K. , Best Error Bond of Quartic Spline Interpolation, J. Appron Theory 58 (1989), 58-67. Davis, P. J. , Interpolation and approximation. New Yrok, 1961. Agrawal, R. P. and Wong, P....

In this paper we develop a polynomial spline approximation for data in Euclidean space. The approach considered involves generating an abstract set which provides a unique parametrization of the geometry of the data considered. Polynomial functions from this set to Euclidean space are considered which provide an interpolation function whose computational cost grows at worst iineruly with the di...

The paper is concerned with computing the B-spline basis of a multi-degree spline space, namely space piecewise functions comprised polynomial segments different degrees. To this aim, we provide general method to work out matrix representation relating sought another one easier compute. This will allow us, for example, calculate multi degree starting from local Bernstein bases degrees or where ...

In this paper we consider polynomial splines with equidistant nodes which may grow as O|x|. We present an integral representation of such splines with a distribution kernel where exponential splines are used as basic functions. By this means we characterize splines possessing the property that translations of any such spline form a basis of corresponding spline space. It is shown that any such ...

Fitting of uncertain data, that is, fitting of data points that are subject to some error, has important applications for example in statistics and for the evaluation of results from physical experiments. Fitting in these problem domains is usually achieved with polynomial approximation, which involves the minimization of an error at discrete data points. Norms typically used for this minimizat...