NB. [Session started: 2006 2 22 18 27 38.253] eqn0=: 3 : '+/*:y.' NB. Set up equations eqn1=: 3 : '*/2-/\y.,{.y.' diffeqns=: 3 : '(eqn0 y.)-eqn1 y.' NB. and differencer. NB. Pick wide range of random arguments... (<./,>./)rndn=. (_1e4+?1e5\$20001)%>:?1e5\$1e3 _9879 9658 (<./,>./)|diffs=. 3 diffeqns\rndn 0.010086928 5.5282426e10 close1s=. 10{./:|diffs NB. Pick 10 closest results as seeds=. close1s{3[\rndn NB. starting points... _0.63838384 0.37931034 _17.451852 _6.4783599 5.4468339 6.1741868 . . . _0.10789474 0.10091743 0.3027933 diffeqns"1 seeds 0.010086928 0.011770021 _0.023991408 ... 0.096197183 NB. Start with 1st seed and look a little bit around it in 3-space: \$&.>nn=. (0{seeds) +&.>/ 0 0 0 to NB. include original point so we can do no worse). \$>>,&.>/&.>/ nn 11 11 11 3 <./,|dd=. diffeqns&> >,&.>/&.>/ nn 0.006545809 NB. This is an improvement. Point on which it is based: >ix=. <(\$dd)#:(,|dd)i.<./,|dd 5 5 0 NB. Value of the new point: >ix{>,&.>/&.>/ nn _0.63838384 0.37931034 _17.461852 diffeqns >ix{>,&.>/&.>/ nn NB. Check it... 0.0065475394 NB. Use this point as new centroid for tighter neighborhood: nn=. (>ix{>,&.>/&.>/ nn) +&.>/ >,&.>/&.>/ nn 0.00054704513 NB. Is further improvement... >ix=. <(\$dd)#:(,|dd)i.<./,|dd 5 5 4 >ix{>,&.>/&.>/ nn NB. New point... _0.63838384 0.37931034 _17.481852 NB. and so on until no significant improvement. NB. Start with another seed... nn=. (1{seeds) +&.>/ >,&.>/&.>/ nn 0.011770021 diffeqns 1{seeds 0.011770021 NB. No improvement, so tighten the search neighborhood: nn=. (1{seeds) +&.>/ >,&.>/&.>/ nn 0.0029753954 >ix=. <(\$dd)#:(,|dd)i.<./,|dd 8 4 4 >ix{>,&.>/&.>/ nn _6.4450266 5.4135006 6.1408534 NB. Tighter around better point... nn=. (>ix{>,&.>/&.>/ nn) +&.>/ >,&.>/&.>/ nn 9.0611054e_5 >ix=. <(\$dd)#:(,|dd)i.<./,|dd 3 12 12 >ix{>,&.>/&.>/ nn _6.4455266 5.4145006 6.1418534 NB. And so on...