ABSTRACT
The n x n tridiagonal matrix T can be stored as an n x 3 matrix A' since there is no need to store the zeros. The first column of matrix A', elements a; I' corresponds to the subdiagonal of matrix T, elements aU-I' The second column ofm~trix A', elements a;.2' corresponds to the diagonal elements of matrix T, elements ai,i' The third column of matrix A', elements a;.3' corresponds to the superdiagonal of matrix T, elements aU+I' The elements a'l,l and a;,.3 do not exist. Thus,
When the elements of column I of matrix A' are eliminated, that is, the elements a; I' the elements of column 2 of matrix A' become '
(i = 2, 3, ... , n)
I I al,2 = al.2 a;.2 = a;.2 - (a;.I/a;_1.2)a;_1.3
The b vector is modified as follows:
bl =b l bi = bi - (a;.I/a;_1.2)bi_1
(i = 2,3, ... , n) (1.150a) (1.I50b)
After a;,2 (i = 2,3, ... , n) and b are evaluated, the back substitution step is as follows: x" = b,,/a;,.2 Xi = (bi - a;.3Xi+I)/a;.2 (i=n-l,n-2, ... , I)
(1.152a) (1.152b)
Example 1.17. The Thomas algorithm.
