A Multipreconditioned Conjugate Gradient Algorithm
Robert Bridson, Chen Greif · SIAM Journal on Matrix Analysis and Applications · 2006
We propose a generalization of the conjugate gradient method that uses multiple preconditioners, combining them automatically in an optimal way. The algorithm may be useful for domain decomposition techniques and other problems in which the need for more than one preconditioner arises naturally. A short recurrence relation does not in general hold for this new method, but in at least one case such a relation is satisfied: for two symmetric positive definite preconditioners whose sum is the coefficient matrix of the linear system. A truncated version of the method works effectively for a variety of test problems. Similarities and differences between this algorithm and the standard and block conjugate gradient methods are discussed, and numerical examples are provided.