Biconjugate gradient method

The biconjugate gradient method is an algorithm in numerical linear algebra for solving systems of linear equations of the form Ax equals b. It differs from the conjugate gradient method in that it does not require the matrix A to be self-adjoint; instead it needs multiplications by the conjugate transpose of A. In its stated form the algorithm begins by choosing an initial guess for the solution, two other starting vectors, one of them associated with the right-hand side, and a preconditioner, and then proceeds iteratively from the first residual. Because the matrix need not be self-adjoint, the method extends the conjugate gradient idea to more general systems of linear equations.