Theme 11. Approximation. Linear and quadratic approximations. Spline approximation

Spline approximation reduces to the construction of segments of curves of low orders (usually of the 3rd order), which approximate the given nodes and bind to each other in the first or second order of smoothness.

A split is called a function that, along with several derivatives, is continuous on the segment [a, b], and on each private interval of this segment [xi, xi + 1] separately are some polynomials of low degree.

Spline interpolation resembles a Lagrangian that requires only values ​​in nodes, but not its derivatives.