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Given an initial approximation <&0 to the fundamental matrix of solutions for = A(t), it is shown that a left correction, T^o, is locally more accurate than a right correction, ^oT. For each relative error function considered, there is a left correction r and the associated differential equation. The common feature is the same integrable part whose forcing function is the difference between L-derivatives of the exact and the initial solution. Upon transformation into a Volterra integraldoi:10.1090/qam/1999836 fatcat:u4lojhopujfz3jgjlyfnhyh3aq