Efficient change of initial conditions, dual chandrasekhar equations, and some applications

We give simple proofs of formulas for converting linear least-squares filtered and smoothed estimates derived for one set of initial conditions to estimates valid for some other set. These are then used to study the possible advantages of first deliberately mischoosing the initial conditions so as to allow computational benefits to be obtained by using certain fast algorithms. In the course of this application we also obtain a new "dual" set of Chandrasekhar equations that provide a fast algorithm for fixed-point smoothing.