       Re: Another basic (?) question about RecurrenceTable and replacement

• To: mathgroup at smc.vnet.net
• Subject: [mg122415] Re: Another basic (?) question about RecurrenceTable and replacement
• From: Dana DeLouis <dana01 at me.com>
• Date: Fri, 28 Oct 2011 05:33:00 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```... using RecurrenceTable and computing sol[n/10,x[n],y[n]] only once ?

Hi.  I don't have a solution, but perhaps a few ideas.
My guess is that using RecurrenceTable and FindRoot might not work well together.  My thinking
is that a Recurrence table uses more exact values, whereas FindRoot returns values at machine precision.

> I kind of got confused with my notations : I want to solve
> x_0 = -2, y_0 = 0

As a suggestion,  perhaps refer to the RSolve function.
That function uses a specific way to refer to previous values.
As a simple example, here are begging x & y values, and recurrence functions:

equ={
x==0,
x==1,
x[n]==x[n-2]+x[n-1],

y==1,
y[n]==n*y[n-1]
};

Rsolve suggest a function for both x & y as a function of n.

RSolve[equ, {x[n],y[n]}, n]  //FullSimplify

{
x[n]->Fibonacci[n],
y[n]->Pochhammer[1,n]
}

Perhaps one of a few suggestions for your example might be to use your FindRoot function and generate a list of x & y pairs.
Round to something more exact if your can.
For example, suppose FindRoot gave the following x & y pairs :

z={{1, 2.00001},{2, 4.9999999},{3, 10.00000001},{4, 19},{5, 36},{6, 69},{7, 134}};

If it is acceptable, try to round the values to something like this:

z={{1,2},{2,5},{3,10},{4,19},{5,36},{6,69},{7,134}};

I don't see a pattern, but FindSequenceFunction did.

FindSequenceFunction[z,n]

-1+2^n+n

I hope I understood your question correctly.
= = = = = = = = = = = = = = = = = = = = = =
HTH
Dana DeLouis
\$Version
8.0 for Mac OS X x86 (64-bit) (February 23, 2011)

On Oct 25, 6:19 am, victorphy <vba... at gmail.com> wrote:
> Hello,
>
> here is another question I could'nt find the asnwer on the web,
> altough I guess it's very elementary.
>
> Here is my problem. Assume I want to solve an implicit equation on two
> variables :
>
> x_0 = _2, y_0 = 0
>
> (x_{n+1},y_{n+1}) = sol(n/10,x_n,y_n)
> for n = 1..10
>
> where f cannot be defined explicitely but is given by something like
> (I give  a silly exemple):
>
> f[x_, a_] := -(x - a)^3 + (x - a)
> sol[a_?NumericQ, b_?NumericQ,c_?NumericQ] := FindRoot[{f[x, a], x +
> y}, {x, b}, {y, c}]
>
> What is the way to write this using RecurrenceTable and computing
> sol[n/10,x[n],y[n]] only once ? (as in the real life the rootsearching
> is longer than above) ?
>
> Any help would be very welcome.
>
> Thank you very much in advance.
>
> Best regards,
>
> Victor

```

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