A renumbering method to decrease matrix banding in equations describing branched neuron-like structures

The solution to matrix equations which describe branched neuron-like structures can be made more efficient by minimizing matrix banding. This can be accomplished through the reordering of the compartmental numbering system. The renumbering method presented here extends upon the numbering method of Hines ((1984) Int. J. Biomed. Comput., 15: 69-76). A demonstration of efficient numbering will be presented for several general cases of branching structures. Theoretical computational savings can be estimated for the above structures. An algorithm to renumber a matrix already in Hines form will be described. Branched nerve equations, electrical networks and chemical reaction models are examples of systems which can benefit from this application.