Please see equation (2.7) of the article (attached for reference). I am particularly interested in understanding the process and in knowing what equation (2.7) would look like in the case of quarterly to monthly interpolation.
It is probably not necessary to go into each detail of the way in which this would be solved by a computer, but an outline of how this equation would be derived in the quarterly to monthly case would be very useful. I would greatly welcome your explanation of this last step.
The problem of taking quarterly data and interpolating monthly data from them has been set up, and most of the matrices needed in the process of carrying out the interpolation have been determined (and explained in detail). The final solution, however, has not been found, since I ran into a snag and couldn't figure out what the next step should be.