  We present an easy implementable algorithm for approximating the geometric
measure of entanglement from above. The algorithm can be applied to any
multipartite mixed state. It involves only the solution of an eigenproblem and
finding a singular value decomposition, no further numerical techniques are
needed. To provide examples, the algorithm was applied to the isotropic states
of 3 qubits and the 3-qubit XX model with external magnetic field.
