Development and Verification of Nuclear Calculation Methods for ...

- 19-
A D » =(A L +A^)«* k. (4.20)
from which follows the block Jacobi iterative method
,. = A^A^-A^,._, + A^1 k , (4.21)
B
B is the block Jacobi matrix.
Similarly the block successive overrelaxation iterative method is defined
by (ref. 14)
tj = (I - «A^ A L )-' {»A" 1 A u+ (|_.) I j f ] _, +
»(I - «A£' A L )-' A^1 k . (4.22)
where L H is the block successive overrelaxation matrix. I is the unit
matrix and u the relaxation factor 0 ( u ( 2. When I < w (• ( 1),the
iteration scheme (4.22) is referred to as overrelaxation (underrelaxation).
4.2.3. The Optimum Relaxation Factor
The fundamental convergence accelerating method for the inner iterations
is that of finding the value of «• = «. that maximizes the rate of
convergence, or in other words minimizing of the largest eigenvalue, the
spectral radius i»(L ), for the L matrix relating successive error vectors.
with
«j° L „«j.1 < 4 - 83 >
e j"
9 i~ *J-i '
l4 " 24,
A is a consistently ordered 2-cyclic matrix, and the relationship between
any eigenvalue i» (L ) for the L matrix and Its associated eigenvalue
u(B) for the Jacobi matrix B Is as follows: