Matrix A is a typical block periodic tri-diagonal matrix
, where [a.sub.i], [b.sub.i], [c.sub.i], t, and s are all m square matrices.
where toeplitz(k), hilb(k), hankel(k), zeros(k), and eye(k) denote the Toeplitz matrix, Hilbert matrix, Hankel matrix, null matrix, identity matrix with orders k, and the elements of matrix ones(*) are one, tridiag([7, 1, -1], r) represents r x r tri-diagonal matrix
produced by vector [7, 1, -1].
[E.sub.x] and [E.sub.y] components are updated implicitly after solving the above tri-diagonal matrix equations.
As implicit directions in the updating step, the implementation of the Mur's first order ABC for [E.sub.x] and [E.sub.y] should be applied inside the tri-diagonal matrix. Taking the [E.sub.x] variable for example, it can be updated by the tri-diagonal matrix when [E.sub.x] (i = 1 ~ [i.sub.max] - 1 / 2; j = 1 ~ [j.sub.max] - 1; k = 0 ~ [k.sub.max]):
Let M and N be a 100 x 100 matrix with element [M.sub.ij] = =1/(i+j+1),(i,j = 1, 2, ..., 100) and a 100 x 100 tri-diagonal matrix
with diagonal elements equal to 4 and off-diagonal elements equal to (=1, =1/2, ..., -1/99) and (1, (r), ...
* The solution for tri-diagonal matrix
takes approximately 1/3rd the number of instructions required for the regular matrix.
is a tri-diagonal matrix
with remaining terms zero.