, more specifically in numerical analysis
, the biconjugate gradient method
is an algorithm
to solve systems of linear equations
Unlike the conjugate gradient method, this algorithm does not require the matrix to be self-adjoint, but instead one needs to perform multiplications by the conjugate transpose .
- Choose , , a regular preconditioner (frequently is used) and ;
- for do
- , ( and are the residuums);
- , .
The BiCG method is numerically unstable
, but very important from theoretical point of view: Define the iteration steps by