SV: [ODE] Iterative solution

[Russ Smith]

you're right, finding the optimal 'w' is a problem. however in my
experiments with a hexapod robot simulation i've discovered that w=1.3-1.4
is usually 'about right'. i'm not sure yet if there's some general
principle behind this (e.g. compute a 'best' constant w based on the
system structure).

as far as constraint order goes, i'm not convinced it makes any
difference (but i've not verified it one way or the other). the
general non-blocking SOR iteration to solve A*x=b is:

  (D+w*L)*x[i+1] = ((1-w)*D-w*U)*x[i] + w*b

where A=L+D+U. the blocking form has a slightly different structure to
D+w*L on the left hand side (i.e. it has some 'U' there too). the point to
note is that regardless of the SOR evaluation order, you still get the
same D+w*L on the lhs (the rows/columns are permuted but the equation
remains basically the same). does this sound right or am i out to lunch
here?

another point that occurs to me is that non-blocking jacobi is not
guranteed to converge on a positive definite matrix, whereas
gauss-siedel/SOR will always converge. in my hexapod experiments the
maximum jacobi eigenvalue often goes above 1.0, the SOR(1)-SOR(2)
eigenvalues never do.

russ.

--
Russ Smith
http://www.q12.org/