Although the order of the linear system (10.28) may be large (indeed, the order tends to infinity as ), its numerical solution is relatively easy owing to the fact that the matrix A shares with the matrices J and B the property of having non zero elements only on the main diagonal and the two diagonals adjacent to It. Matrices of this kind are called tri diagonal. In fact, if , we have by virtue of (10.29)

and for

Linear systems involving non-singular tri diagonal matrices are most easily solved by an adaptation of the Gaussian algorithm which may conveniently be summarized as follows. Assume we have succeeded in determining two nonsingular matrices and of the special form

U =

having the property that

(10.30)