Interpolation and least squares curve fitting

In scientific research and engineering technology, we often encounter function expressions that are too complex to be calculated, and the function values ​​at many points need to be calculated; or a certain function y=f(x) is only known and obtained experimentally or measured ) n+1 x0, x1,...,xn values ​​y0, y1,...,yn that are different from each other in the interval [a, b] need to construct a simple function P(x) as the function y=f The approximate expression of (x) is y=f(x)≈P(x), such that P(xi)=f(xi)=yi, (i=0,1,...,n). This type of problem is interpolation Problem, P(x) is called the interpolation function. Today, with the popularization of electronic computers, the application scope of interpolation method has involved various fields of production, scientific research and so on. Especially due to the needs of practical problems such as aviation, shipbuilding, and precision machining, the interpolation method is particularly important in practice and theory and has been further developed, especially the spline interpolation developed in recent decades. It has also been widely used. In addition, in scientific research and engineering technology, it is often necessary to find the approximate expression of the functional relationship between variables x and y from a set of measurement data (xi, yi) (i=0,1,...,n). And starting from a given set of experimental data, we seek an approximation function y=ρ(x) of the known function, so that the deviation of the approximation function from the known function as a whole can be minimized and measured in a certain way. It does not necessarily pass through all points (xi, yi), that is, least squares curve fitting. This software is designed for these problems, including: linear interpolation, parabolic interpolation, piecewise linear interpolation, piecewise linear interpolation, piecewise parabolic interpolation, Lagrange interpolation polynomial, Newton interpolation polynomial, equidistant node interpolation polynomial "Newton's forward interpolation formula, Newton's postinterpolation formula", Hermitian interpolation, cubic spline interpolation "Spline function expressed by first-order derivatives at nodes (given first-order derivative values ​​at two end points, given two end points The second-order derivative value at the node), the spline function represented by the second-order derivative at the node (the first-order derivative value at the two end points is given, the second-order derivative value at the two end points is given)‖; least squares curve fitting . The software adopts a friendly input and output scheme that allows users to freely input according to a certain format. Please refer to the help document for details on the format. It uses certain graphics processing technology to intuitively display specific data information. Through the combination of good mathematical methods and computer technology, Ensure data reliability. Additionally, you can customize drawing colors.