bo198214 Wrote:Can you make a comparison of with Andrew's computed by your super sophisticated algorithm and post a graph of the difference in the range say [-1,1.9] somewhere?!

If the difference turns into a smooth curve starting from some precision then we know they are different, if the result is at any precision rather a random curve this would favour the equality of both solutions.

I've come back to this. I'm starting with an unaccelerated solution to Andrew's slog, to ensure that my accelerated version doesn't skew the results. Assuming initial results with the unaccelerated version are promising, I'll then work on an accelerated solution.

I did a preliminary test with the rslog calculated with n=80 (i.e., 80 exponentiations), using the first 150 terms of the power series, and a solution to the 500x500 system, and the results were very close, accurate to half a dozen decimal places or so (I didn't save the results).

I've now calculated an rslog solution with n=100, using the first 200 terms of the power series. I've also calculated the solution to a 1000x1000 matrix for Andrew's slog.

Comparing then the first 100 terms of each, the differences were less than about 10^-11 in absolute terms. In relative terms (since the terms decrease in magnitude exponentially), by about the 25th term the difference is about 10^-5. So from an initial testing, it appears quite likely that Andrew's solution and the rslog will converge on the same solution. But as I had previously mentioned, very high precision is necessary to make a strong conclusion, and at any rate this doesn't constitute a proof.

~ Jay Daniel Fox