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| Purpose of the calculations carried out here is to estimate values of many times differentiable real function of real variable in points not too distant from several points in which its values are exactly known. Given n pairs of numbers x,y second of which is the exact value of the examined function in the point represented by the first, we construct a polynomial degree n - 1 or less having in the points x the same values as the the function. The value of the function in any other point is then estimated as equal to the value of the polynomial in that point. First applet constructs the collocation polynomial. Type the pairs of numbers in the left input field,one pair per line, numbers separated by spaces. The click submit. Graph of the polynomial appears above the text fields and the right text field contains the coefficients of the polynomial in column vector form, starting at the top with coefficient at zero power of independent variable and ending with the coefficient at power equal to the degree of the polynomial. Second applet calculates values of any polynomial and its first and second derivative in any point x. Type the coefficients of the polynomial in column vector form in left input field and click enter or click copy to transfer the polynomial found in the first applet to the second. Then type the desired value of the independent variable in the upper right input field and click calculate. To clear any input field under focus pres F2. |
Back to Index Download! Applets:InterpolApplet(NAME="Producer"), PolyEvalApplet