 ### Completion algorithms in estimating the mining reserve

Mineral resource is the accumulation of substances that occur naturally in or on the earth's crust. Determining the boundaries of this resource requires careful study of geology by mapping and geophysics and performing extensive geochemical or geophysical tests on the surface and underground. Drilling is carried out directly as a mechanism for surveying the composition of the content, including calculating the recoverable amount of minerals of a certain degree and / or quality, and determining the value of mineral resources.

In engineering, when a number of data points can be obtained by sampling and experimenting, it is possible to create a function that closely fits these data points. Fortunately, there are numerical techniques that can be applied to estimate a function of the range covered by a set of points (as in basic drill samples), in which the job values ​​are known. Satisfaction is the process of searching for unknown values ​​as the simplest method requires knowing the rate of constant change in two points. For example, any function y = f (x) where the estimation process of any y value, for any intermediate value x, is called interpolation.

One way to estimate missing values ​​is to use "Lagrange polynomial interpolation" . In its simplest form, the degree of a polynomial is equal to the number of points shown minus 1. Mainly, there are three numerical algorithms that are widely used to calculate the Lagrange interpolation: Newton's algorithm, Nevels algorithm and direct map to Lagrange's formula. The selection algorithm varies based on efficiency characteristics such as number of sample points, complexity, and degree of numerical errors.

Another frequently used method of interpolation is "Bulirsch-Stoer interpolation" . This method uses a rational function, i.e. a maximum of a polynomial number, such as R (x) = P (x) / Q (x). Induction in numerical integration is preferable to using polynomial functions because logical functions are able to approximate functions with sample points well (compared to polynomial functions), given that there are sufficient numbers of high-power terms in the denominator to obtain close sample points. This type of job can have a noticeable accuracy.

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The "Cube interpolation" It is widely used in estimating mining reserves. In numerical analysis, spinal interpolation is a form of interpolation using a special type of polynomial polynomial called a slice. This method provides a great deal of smoothness with the variation in data. In fact, in ancient days people drew smooth curves by gluing nails at the site of calculated points and laying flat bars of metal between the nails. The bands were then used as rulers to draw the desired curve. These bars were called splines from metal, where this interpolation algorithm comes from.

With the distinct types of interpolation techniques available, which method to choose? Often it is difficult to choose between these algorithms and there are really many ways to cat skin. The selection criteria that are often accepted depends on the number of sample points where the cubic chip algorithm is preferred when insufficient sampling points are available. If a job is difficult to reproduce, Bulirsch-Stoer fulfillment may be appropriate. Lagrange interpolation is useful when there are a number of medium to large sample points.

The above is a first step in estimating the mining reserve. Many other tasks – minimizing estimation errors, calculating optimal sampling distances, mass score estimates, contour mapping, and estimating the recovery area size are part of the reserve estimation process. Each task has a numerical solution and algorithms are available to calculate the results.

Metal exploration in general is a process that is performed in an attempt to find commercially viable concentrations of ore for profit. In this process, reserve estimation is a more intense, organized and efficient form of mineral exploration. The use of applied mathematics fulfillment algorithms to estimate the mining reserves of the industry provides computer efficiency, reduced time-consuming tasks for manageable units, and solutions that are difficult to achieve otherwise.

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