Lesson 11

The disadvantage of interpolation is that for many nodes a polynomial of high degree is formed.

If the original data were not obtained accurately, then the interpolating function though accurately passes through nodal points, nevertheless is inaccurate. In such cases, an approximation should be used - the definition of the function that closest (best) approaches the nodal points.

Approximation is the finding of the function of the given form y = f (x), which at points x0, x1, x2, .., xn took the value as close as possible to the values ​​y0, y1, y2, .., yn.

The curve f (x) is called the approximating curve or the regression line .

Types of approximating functions:

• Linear y = ax + b;
• The quadratic y = ax ^ 2 + bx + c;
• Degree y = ax ^ m;
• Logarithmic y = a ln (x) + b;
• Rational y = x / (ax + b) and others.