In numerical linear algebra, the conjugate gradient squared method (CGS) is an iterative algorithm for solving systems of linear equations of the form A x = b {\displaystyle A{\mathbf {x}}={\mathbf {b}}} , particularly in cases where computing the transpose A T {\displaystyle A^{T}} is impractical. The CGS method was developed as an improvement to the biconjugate gradient method.