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In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.

In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces.

Sometimes observations in statistical analysis are not independent and typically are correlated with their spatial locations. In spatial statistics there are some methods to interpolate this kind of data. In this paper some of interpolators for spatial data will be studied. Then they will be evaluated and compared by means of mean square errors criteria. Finally it will be shown that kriging acts better than other methods such as spline, inverse distance, for interpolation of spatial data.

Hidden Markov Model is a popular statisical method that is used in continious and discrete speech recognition. The probability density function of observation vectors in each state is estimated with discrete density or continious density modeling. The performance (in correct word recognition rate) of continious density is higher than discrete density HMM, but its computation complexity is very high, especially in very large discrete utterance recognition problems. For real time implementation of very large discrete utterance recognition, we must use discrete density HMM (DDHMM). To increase the performance of DDHMM, one usual solution is fuzzy interpolation. In this study, we present a new method named Gaussian interpolation. We implemented and compared the performance of two types of interpolation methods for 1500 Persian speech command words. Results show that precision and flexibility of Gaussian interpolation is better thanthose of the fuzzy interpolation.

Interpolation and approximation are the most important parts of partial differential equation solution procedures, which significantly affect the cost and the accuracy of the results. This paper is aimed to exhaustively investigate the interpolation algorithms and trace their chronologically developments. The interpolation methods are classified based on their mathematical representation, and then surveyed separately. An abridgement of calculation steps of methods are presented and for details, the reader is referred by the main references. The usage records in applied science and engineering are included and their numerical dominance, stability and convergence rate are discussed.