> On this subject, I have never quite understood the domain of d. > 1 . For example: > > f=:***: > f i:5 > _25 _16 _9 _4 _1 0 1 4 9 16 25 > (f d.1) 2 > |domain error > | (f d.1)2 > > f seems a perfectly reasonable function to differentiate: f' is > continuous. While I would not expect this to be differentiated > symbolically, I would have thought that either polynomial approximation or > secant slope (the methods indicated in the Dictionary) would > work. Or maybe there are stability issues?
f d. 1 is a symbolic differentiator and is table driven plus a few rules. In this case I believe it tried to use the product rule and then foundered on the monad * which is not differentiable. In contrast: (1&o. * 2&o.) d. 1 (2&o. * 2&o.) + 1&o. * -@(1&o.) For * * *: to be differentiable the function itself would have to be in the table. ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Sunday, October 14, 2007 4:29 Subject: Re: [Jgeneral] Brief example To: General forum <[email protected]> > Roger Hui wrote: > > 0. The following is a shorter equivalent for "newton": > > newton=:1 : '- u % u d. 1' > > > Thanks for this: I should have seen it myself. > > > 1. Showing convergents: > > > > 2. Rational numbers: > > > > These are good examples, and I should do them. I would > like to include > ^:_ , since it also shows tolerant equality. > > Thanks, Raul, for the symbolic derivatives. > > On this subject, I have never quite understood the domain of d. > 1 . For > example: > > f=:***: > f i:5 > _25 _16 _9 _4 _1 0 1 4 9 16 25 > (f d.1) 2 > |domain error > | (f d.1)2 > > f seems a perfectly reasonable function to differentiate: f' is > continuous. While I would not expect this to be differentiated > symbolically, I would have thought that either polynomial > approximation or > secant slope (the methods indicated in the Dictionary) would > work. Or > maybe there are stability issues? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
