Published 1. End Conditions for Interpolatory Septic Spline Ghazala Akram and Shahid S. Siddiqi, International Journal of Computer Mathematics, Vol. 82, No. 12, 2005 pp15251540. 2. Solutions of Fifth Order Boundary-Value Problems Using NonPolynomial Spline Technique Shahid S. Siddiqi and Ghazala Akram, Applied Mathematics and Computation Vol. 175, No. 2, 2006 pp. 1574-1581. 3. Solutions of Sixt...

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 ...

In truncated polynomial spline or B-spline models where the covariates are measured with error, a fully Bayesian approach to model fitting requires the covariates and model parameters to be sampled at every Markov chain Monte Carlo iteration. Sampling the unobserved covariates poses a major computational problem and usually Gibbs sampling is not possible. This forces the practitioner to use a M...

In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One these equations, dissipative wave equation, has found a plethora useful applications different fields. A special class solutions studied for equation including exact approximate solutions. The...

We discuss the problem of detecting the location of discontinuities of derivatives of a periodic function, given either finitely many Fourier coefficients of the function, or the samples of the function at uniform or scattered data points. Using the general theory, we develop a class of trigonometric polynomial frames suitable for this purpose. Our methods also help us to analyze the capabiliti...