Hey, Philip, did you get anywhere with problem 1.45? I've been

playing around a little bit, but I can't seem to find a general

solution for nth root greater than 4. Either the damping is too large

(or at least wrong) as to cause the result to be wrong, or the damping

is "incorrect" and the fixed-point never converges.

I'm done with this problem as I feel that I've learned the real lesson

of the section, but I was just curious if you did come up with a

solution.

--

Charles

On 5/1/05, Philip Ansteth <pansteth@...> wrote:

> --- In sicp-vsg@yahoogroups.com, "Philip Ansteth" <pansteth@y...> wrote:

> > Does anybody have an solution yet?

> >

> > I'm close, I think, but . . . .

>

> I think I now have the main solution, namely a "simple" procedure for

> computing nth roots using fixed-point, average-damp, and the repeated

> procedure.

>

> However, several questions remain.

>

> First, there is the issue of the number of average dampings to use.

> My hypothesis (i.e., it can be one less than n) can be "empirically"

> confirmed with various tests. Does the problem demand that one

> demonstrate such a hypothesis?

>

> Also, I confess I don't know whether all functions whose value at

> y is x / y^(n-1) even have fixed points that can be calculated

> this way. I guess it is something I should already know, or that I

> could look up, or that I could figure out for myself. But I'm

> hoping somebody in the group who knows will just tell me.

>

> Part of my question stems from my wariness about the authors'

> wording. I keep getting tripped up by my own haste or, IMHO,

> their sloppiness. (They've been imprecise about Ackermann's function

> and the "congruence" terminology, for example.)

>

> So when they say, on page 68, "For some functions f we can locate a

> fixed point by . . .", I don't know the force of the word "some".

>

> Does anybody know what they're referring to? (I think of

> the precision with which they expressed the order of growth function

> on page 43. Is the statement on 68 on the save level?)

>

> Or, to express the above questions in another light, Could one use the

> answer to 1.45 as a safe substitute for the built-in expt?