ABSTRACT
This chapter provides an introduction to the Lanczos procedure for generating equivalent cables. In a limited test of complex trees, we have found no single algorithm to give significant advantage over the others when generating equivalent cables. In the Lanczos procedure, the one-dimensional linear cable equation, a second order partial differential equation, is employed to devise a set of discrete cable equations which can be used to form a matrix representation of a dendritic tree. The Lanczos procedure assumes that dendritic tree segments can be described effectively by the one-dimensional linear cable equation. The observed complexity and variety of neuron dendritic geometry has raised interesting questions concerning the role that such structures might play in neuronal signal processing. In the multi-cylinder model, the branches of a dendritic tree have been divided up into distinct uniform cylinder sections. A well chosen numbering system makes the Lanczos transformation simpler to implement and computationally more efficient.
