5.1.1 Sequential algorithm

If matrix $K$ in (5.1) is symmetric (i.e., $K=K^T$) and positive definite (i.e., $(K\underline{v},\underline{v})_{L_2} > 0$), then we may use the CG method for solving (5.1). Algorithm 5.1 presents this method in combination with a preconditioner $C$.

Vectorization of the classical CG ($\;C=I$) is trivial but the use of a preconditioner may cause troubles (see also 5.8). The same holds for parallelization.