Introduction: To estimate the accuracy levels of Lagrange, Newton backward interpolation, and linear interpolation methods in estimating the output factors for square fields used in linear accelerator for 6 MV photons at various depths. Materials and Methods: Ionization measurements were carried out in radiation field analyzer in linear accelerator for 6 MV beams at the depths of 5 and 10 cm by 0. 6 cc Farmer-type ionisation chamber. Dosimetry was performed by ion collection method with 0. 5 cm2 interval for square fields from 4 × 4 cm2 to 40 × 40 cm2 field sizes. The measured output factor values for 10 square field sizes with equal interval were taken for interpolating the intermediate square field size values. The Lagrange and Newton backward methods were used for predicting the intermediate output factors. Results: The percentage of deviation from the measured value was estimated for all the three methods. The calculated output factor values of the two proposed methods were compared with the standard linear interpolation method used in routine clinical practice. It was observed that the Lagrange and Newton backward methods were not significantly different from the measured value (P=0. 77). The linear interpolation values were significantly different from the measured value (P<0. 01). Conclusion: It is recommended to use the Lagrange and Newton backward interpolation methods to estimate the intermediate output factors to increase accuracy in treatment delivery. The routine linear interpolation method can be applied only for small intervals. This proposed interpolation method is highly associated with the measured values in all the interval levels.

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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.

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.