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The purpose of this paper is to develop and generalize the improved method of grids (method of finite differences) described in (Kollats, 1969) to calculation a partial derivative. The method of uncertain coefficients is applied to the two dimensional boundary value problems. For obtaining of interpolation polynomials, the matrixes are used. The essential simplification of the calculation formulae is received. The numerical results are presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to generalize the method of finite differences described in (Kollats, 1969). For obtaining of interpolation polynomials, the matrixes and method of uncertain coefficients are used. The essential simplification of the calculation formulae is received; in particular case they are the L. Kollats' formulas. The accuracy of the used approach is estimated in same way as it is made in the classical method of finite differences. The use of matrix symbolics gives the convenient tool for realization of calculations by computers. The numerical results are presented as well. The received results can be applied to the solution of boundary value problems of various classes and to increase the accuracy of the finite elemet method. [ABSTRACT FROM AUTHOR]

In this paper work are presented the performances of three interpolation methods of sparse time series from the correlation point of view. The values of the time series represents the dam crust displacements measured for the same target (measuring) points. The two kinds of dam displacements time series are generate from two different measuring systems involved in dam monitoring process. One time series is a very large numbered and the other has just a few value and is a sparse time series. There is presented the comparison of the Fourier based correlation results between the large numbered time series and the sparse interpolated ones with the radial basis function, cubic spline and Fourier interpolation methods. [ABSTRACT FROM AUTHOR]

This paper presents the volume calculation starting from two vertical 3D scanned walls with non-matching vertical planar projections (grids). The vertical walls of an open mine have unregulated shapes which were taken in different moments. From the scanned point clouds the 3D contours of the vertical walls are extracted. The resulted 3D object has two 3D wall surfaces with high resolutions and four coverage surfaces (upper, lower, right and left). This is done considering the conjugate parts of the walls contours and the RBF (radial basis function) 3D interpolations of all the walls. The volume is calculated by sliced surface and height resolution multiplying, over the entire set of slices that builds up the 3D resulted object. [ABSTRACT FROM AUTHOR]

In the class of the investigation instruments offered by the numerical analysis, a particular role is performed by the interpolation methods. We can notice that most of the so-called classical analytic models can nowadays be used in computer based approaches as components of some more complex hybrid models. Interpolation, as a part of the numerical methods is used in all the sub-models of a complex model and the performance of the implementations have an important overall influence. The paper presents several ideas regarding the interpolation instruments employed in computer based models in engineering, weak point of some software applications which offer this kind of facilities and functionalities which should be implemented in the next generation software. [ABSTRACT FROM AUTHOR]