How to find a function knowing only points?

Question

Algorithms

Suppose I have a set of values ​​​​on the XY plane, tell me how to find a function for these points or advise what kind of literature in this direction

Answer 1

Try here .

Answer 2

Apparently, what you are talking about is an approximation of a function. Wikipedia has a more detailed article on interpolation .
In fact, your task is reduced to 2 steps:
1. Based on points and common dependencies, the form of the function is selected (for example, polynomial, exponential, etc.).
2. A model is built in which a function with unknown parameters is specified. The task is to find such parameters in order to minimize the residual function (often this is the square of the difference between the real values ​​​​at given points and the values ​​\u200b\u200bof the model function, see LSM ).

Answer 3

Here's a great iPad app. Helps me out.
DataAnalysis
Perfectly copes with such tasks and FREE.
Application site

Answer 4

Yes, these are numerical methods. Search for "Approximation" and "Interpolation". From the books I can recommend: Dyakonov V.P. Reference book on algorithms and programs in BASIC for personal computers. I have the 1989 paper edition. You can find it on Google at DJVU. Examples in BASIC allows you to program the desired method in your favorite programming language, without even delving into their essence. In general, if you have time and desire, figure it out, it's quite interesting :)

Answer 5

There is also such a thing as symbolic regression :
https://habrahabr.ru/post/163195/

Answer 6

If some values ​​of x and y are known on the graph, then you can find the coefficient and free term of this function. Let's assume a linear dependence y=kx+b. For example, we know that at x = 2, y = 5 and at x = 3, y = 4.5. Let's compose a system of equations by substituting the known values ​​of x and y: {2k+b=5; 3k+b=4.5}, having solved the system, it is easy to guess that k=-0.5; b=6;
As a result, our function takes the form y=-0.5x+6