approximation

Polynomial Approximation (Least Squares Method)

Approximates a set of data points using polynomial functions via the least squares method with Gaussian elimination.

Usage

1. Prepare test.txt with data points (one per line):

   x1 y1
   x2 y2
   ...
   

2. Compile:

   g++ -o main main.cpp

3. Run and enter polynomial degree (max 5):

   ./main

Example

Input (test.txt):

-1.8 5.68
-1 1.99
0.2 1.24
1.2 9.81
2 14.5

Output (degree 2):

The sought coefficients are:
x^0 = 1.973
x^1 = 2.164
x^2 = 2.269

The sought approximating function is:
F(x) = + (1.973)x^0 + (2.164)x^1 + (2.269)x^2

Result: F(x) = 1.973 + 2.164·x + 2.269·x²

Algorithm

• Builds system of normal equations
• Applies Gaussian elimination with partial pivoting
• Performs back substitution to find coefficients
• Uses vectors for dynamic array sizes