efficient structural analysis and to free the Index Display Matrix from

its dependence upon the function index range the concept of the

"blocking factor" is introduced. The blocking factor for a function

index is the number of rows which will be included in the IDM for

variable indices which depend upon that function index. If the function

index ii above were assigned a blocking factor of 3 then the IDM for j1

would be:

 0 1 2 3 4

 1 x xx

 2 X X X
 2 x x x

 3 x xx

This Index Display Matrix conveys the notion of a tri-diagonal matrix

while occupying considerably less space both on paper and in any data

structure used in computer implementation. Since the blocking factor is

arbitrary and is defined by the person defining a problem it should be

pointed out that the blocking factor must be large enough to avoid any

ambiguity in describing the IDM. In particular a blocking factor of 1

should never be used.


2.4 Tndex Imbedding

 The value of Function-Variable Incidence Matrices and Index

Display Matrices is that while they are considerably smaller than the

actual incidence matrix which they represent, they contain all of the

inorrmation contained in the incidence matrix. This can best be illus-

trated by the fact that the incidence matrix can be constructed from the

Function Variable Incidence Matrix and its Index Display Matrices.