  We discuss the distributed matching scheme in accelerators where control of
transverse beam phase space, oscillation, and transport is accomplished by
flexible distribution of focusing elements beyond dedicated matching sections.
Besides freeing accelerator design from fixed matching sections, such a scheme
has many operational advantages, and enables fluid optics manipulation not
possible in conventional schemes. Combined with an interpolation scheme this
can bring about a new paradigm for efficient, flexible, and robust optics
control. A rigorous and deterministic algorithm is developed for its
realization. The algorithm is a matching tool in its own right with unique
characteristics in robustness and determinism. The beam phase space dynamics is
naturally integrated into the algorithm, instead of being treated as generic
numerical parameters as in traditional schemes. It is applicable to a wider
range of problems, such as trading-off between competing options for desired
machine states.
