PCG Preconditioned Conjugate Gradients Method is a replacement of the standard built-in PCG code. Two new options are implemented: flex and null . The flex option changes the standard PCG algorithm into the flexible one. It allows using sophisticated preconditioning, not limited to the traditional fixed SPD preconditioners, as required by the standard PCG.



With the null option, the code attempts to compute a nontrivial solution X of the homogeneous system of linear equations A*X=0. Here, the coefficient matrix A must be Hermitian and positive semi-definite. If the null-space of A is more than one dimensional, i.e. A*X=0 allows multiple linear independent solutions, the code still converges to one solution, namely, the projection of the initial guess to the null-space.



Without the new options, the new PCG code works exactly the same way as the latest revision of the built-in PCG-PCG Preconditioned Conjugate Gradients Method is a replacement of the standard built-in PCG code. Two new options are implemented:　flex　and　null . The　flex　option changes the standard PCG algorithm into the flexible one. It allows using sophisticated preconditioning, not limited to the traditional fixed SPD preconditioners, as required by the standard PCG.



With the　null　option, the code attempts to compute a nontrivial solution X of the homogeneous system of linear equations A*X=0. Here, the coefficient matrix A must be Hermitian and positive semi-definite. If the null-space of A is more than one dimensional, i.e. A*X=0 allows multiple linear independent solutions, the code still converges to one solution, namely, the projection of the initial guess to the null-space.



Without the new options, the new PCG code works exactly the same way as the latest revision of the built-in PCG