  We investigate the optimal dynamical decoupling sequence for a qubit coupled
to an ohmic environment. By analytically computing the derivatives of the
decoherence function, the optimal pulse locations are found to satisfy a set of
nonlinear equations which can be easily solved. These equations incorporates
the environment information such as high-energy (UV) cutoff frequency \omega_c,
giving a complete description of the decoupling process. The solutions explain
previous experimental and theoretical results of locally optimized dynamical
decoupling (LODD) sequence in high-frequency dominated environment, which were
obtained by purely numerical computation and experimental feedback. As shown in
numerical comparison, these solutions outperform the Uhrig dynamical decoupling
(UDD) sequence by one or more orders of magnitude in the ohmic case.
