Conjugate gradient squared method

In numerical linear algebra, the conjugate gradient squared method (CGS) is an iterative algorithm for solving systems of linear equations of the form

, particularly in cases where computing the transpose

[2][3][4] A system of linear equations

To solve the system is to find the value of the unknown vector

[3][5] A direct method for solving a system of linear equations is to take the inverse of the matrix

Iterative methods begin with a guess

Once the difference between successive guesses is sufficiently small, the method has converged to a solution.

[6][7] As with the conjugate gradient method, biconjugate gradient method, and similar iterative methods for solving systems of linear equations, the CGS method can be used to find solutions to multi-variable optimisation problems, such as power-flow analysis, hyperparameter optimisation, and facial recognition.