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"Hybrid block GMRES" means that the solver first runs block GMRES. It stores the resulting coefficients, which form a matrix polynomial. It then can reuse this polynomial for subsequent solves. This avoids the cost of the inner products and norms in GMRES. However, the resulting polynomial is not necessarily as effective as the equivalent number of GMRES iterations.

We call solvers that take this approach "seed solvers." Belos implements both a Block GMRES seed solver (this class) and a CG-based seed solver (Belos::PCPGSolMgr).

Here is a list of all the parameters that this solver accepts:

Like all Belos solvers, parameters have relative or "delta" semantics. This means the following:

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