In theory, the linear least squares problem is simple to solve, it is just a matter of solving the linear system of equations \(A^\top A \, x = A^\top b\) . In practical applications, the matrix A usually has many rows, so solving with pencil and paper is no longer possible. But even the (naive) solution of the normal equation with a computer is not recommended: The calculation of \(A^\top A\) and subsequent solving of the LGS \(A^\top A \, x = A^\top b\) is unstable and thus leads to inaccurate results. In the numerical solution of the linear least squares problem, the QR-decomposition of the matrix A is helpful. With the QR-decomposition, the linear least squares problem can be solved numerically stable.