  In this paper we present a new family of approximate Riemann solvers for the
numerical approximation of solutions of hyperbolic conservation laws. They are
approximate, also referred to as incomplete, in the sense that the solvers
avoid computing the characteristic decomposition of the flux Jacobian. Instead,
they require only an estimate of the globally fastest wave speeds in both
directions. Thus, this family of solvers is particularly efficient for large
systems of conservation laws, i.e. with many different propagation speeds, and
when no explicit expression for the eigensystem is available. Even though only
fastest wave speeds are needed as input values, the new family of Riemann
solvers reproduces all waves with less dissipation than HLL, which has the same
prerequisites, requiring only one additional flux evaluation.
