Embedded Systems September 2000 Vol13_10

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and the same operations are done in pre tty much the same places. Somewhat surprisingly, though, they are not exactly identical. Nor do they pe r form ide ntically. On the same problem, my structured ve rsion of fmin.f took 11 iterations to converge to doubl e-precision accuracy. T he RecifJes version, brent. c, took 19 ite ra- tion to converge to only single-preci- ion accuracy. At thi s poin t in my trek, I am com- ple tely bummed out. I suppose, for the sake of comple teness, I should have been spending my summe r vacatio n compa ring th e two pro- grams and trying to discover the rea- son why th e Fo rtran ve rsio n con- verges nearly twice as fast. I didn 't. To be brutally honest, I don't really care anymore. I've seen all of Bre nt's me thod I want to see. Can we improve on Brent? When I began this odyss y, it was certa inly n ot my inte nti on to try to invent th e world 's greatest second- o rde r minimizati on algorithm. And 1 must ay, I feel pre tty ne rvous about a ttempting it. Thi is not the kind of thing on e does casuall y. A lot of users out th e re wa nt good algorithms, and if my offe ring turns o ut to have one or mo re fata l fl aws, you can be sure I'm going to be hearing from them in droves. I'm sure to make van Snyde r 's hit list. H wever, at thi s point, I d on ' t see tha t I have much of an a lternative. My goal has always been to give you a method tha t not only wo rks, but that I can expl ain to you ra tio nall y. [[I can ' t explain Bre nt, I'll ex pl ain Crenshaw. There's also no way I can spend the kind of time Brent presumably pent on his dissertation proj ect. To come up with the perfect algorithm, one hould run it on as many diffe rent kinds o [ problems as possibl e, looking fo r the cases that give it tro uble, and then patching it up to deal with them. I don't have time to do that he re. Embedded Systems Programming SEPTEMBER 2000 39

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