Multivariate Approximation and Splines

This book contains the refereed papers which were presented at the interna­ tional conference on Multivariate Approximation and Splines held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit­ ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul­ the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul­ tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non­ linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.