  The paper establishes a direct linearization scheme for the SU(2)
anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of
linear integral equations with general measures and plane wave factors. After
introducing infinite-dimensional matrices as master functions, we are able to
investigate evolution relations and recurrence relations of these functions,
which lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM
equation in the Euclidean space and two ultrahyperbolic spaces by reductions to
meet the reality conditions and gauge conditions, respectively. Special
solutions can be obtained by choosing suitable measures.
