Fixed Coefficients

There is an issue dealing with the fixed coefficient of $\bold p$, that I believe is not a problem, but I place it under ``future work'' anyway because I expect it to come up occasionally. Our PEFs, $\bold a$, have a fixed coefficient that is defined to have the value 1. We actually estimate $\bold p$, which is related by $\bold a=\bold S\bold p$, which means we should load our initial model guess, $\bold p_0$, with some other value in the fixed coefficient, that will be integrated by $\bold S$ to give 1's. This is a hassle because our software has the value 1 built in. Luckily, the problem seems to disappear. Wherever the forward operator is applied, it looks like $\bold Y \bold K \bold S \bold p$, which is the same as $\bold Y \bold K \bold a$.The adjoint is used to calculate the change in the roughened model variable $\bold p$: $\bold \Delta \bold p = \bold S' \bold K' \bold Y' \bold r$, where $\bold r$ is the residual. Whatever change is made to the fixed coefficient is zeroed by $\bold K'$.In other words, it seems we never need to know the fixed coefficient of $\bold p$.