We develop array algorithms for H/sup /spl infin// filtering. These algorithms can be regarded as the Krein space generalizations of H/sup 2/ array algorithms, which are currently the preferred method fur implementing H/sup 2/ filters. The array algorithms considered include two main families: square-root array algorithms, which are typically numerically more stable than conventional ones, and fast array algorithms which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H/sup /spl infin// filters, as these conditions are built into the algorithms themselves. However, since H/sup /spl infin// square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H/sup 2/ case, further investigation is needed to determine the numerical behavior of such algorithms.