In this work, a new type of Interpolation formula is introduced. These formulas can be an extension of the Lagrange Interpolation formula. The error of this new type of Interpolation is calculated. In order to display efficiency of the proposed formulas, three numerical examples are presented.

In this work, using the determination function, some new kinds of Interpolation formulas are presented.These novel formulas are extensions of Lagrange Interpolation. Error formula for these new kind of Interpolation formulas are obtained. Finally, using these formulas, some new numerical integration formulas in closed-type and open-type are presented. Absolute error of quadrature formulas show the efficiency of the proposed formulas.

Image zooming is one of the important issues of image processing that maintains the quality and structure of image. Zooming an image necessitates placing the extra pixels in the image data. Moreover, adding the data to the image must be consistent with the texture in the image in order to prevent artificial blocks. In this study, the required pixels are estimated using barycentric rational Interpolation. The proposed method is a non-linear one which can preserve the edges and reduces the blur and block artifacts on the zoomed image. Numerical results are presented using PSNR and SSIM fidelity measures and they are compared to some other methods. The average PSNR of the original image and image zooming was 33. 08 which can prove that image zooming is very similar to the original image. The experimental results reveal that the proposed method has a better performance compared to other methods and can provide good image quality.

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.