Interpolation is process of search of intermediate values of any given size on separate known values of this size. This process finds application, for example, in mathematics for search of value of the f (x) function in points x.
It is required to you
- Programs of creation of schedules and functions, calculator
Instruction
1. Often when carrying out empirical researches it is necessary to face a set of the values received by method of random sampling. It is required to construct a function graph into which with the maximum accuracy also other received values will fit of this number of values. This method, to be exact the solution of this task is approximation of a curve, i.e. replacement of some objects or phenomena by others, close in initial parameter. Interpolation, in turn is a kind of approximation. Interpolation of a curve call process at which the curve of the built function passes through the available points of data.
2. There is a task, very close to interpolation, which essence will consist in approximation of initial difficult function by other, much simpler function. If separate function is very difficult for calculations, then it is possible to try to calculate its value in several points, and on the obtained data to construct (to interpolate) simpler function. However application of the simplified function will not allow to obtain so exact and reliable data what initial function would give.
3. Interpolation through an algebraic binomial, or linear interpolyatsiyav a general view: there is an interpolating of some set f (x) function accepting value in points of x0 and x1 of a piece [a, b] an algebraic binomial of P1 (x) = ax + b. If it is set more than two values of function, then required linear function are replaced linearly - piecewise function, each part of function consists between two preset values of function in these points on the interpolated piece.
4. Interpolating by method final raznosteydanny method one of the simplest and widespread methods of implementation of interpolation. Its essence contains in replacement of differential coefficients of the equation by differential coefficients. This action will allow to pass to the solution of the differential equation with a solution of its differential analog, in other words, to construct its final and differential scheme
5. Construction a spline-funktsiisplaynom in mathematical modeling call the piecewise set function which coincide with the functions having simpler nature on each element of splitting the range of definition. The spline from one variable is under construction by splitting a range of definition into final number of pieces, and, on each of which the spline will coincide with some algebraic polynom. The maximum degree of the used polynom is spline degree. A spline function are applied to a task and the description of surfaces in various systems of computer modeling.