Re: Re: Iterative application of FindRoot with adjusted started values

• To: mathgroup at smc.vnet.net
• Subject: [mg33022] Re: [mg33007] Re: Iterative application of FindRoot with adjusted started values
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Tue, 26 Feb 2002 04:35:07 -0500 (EST)
• Organization: JEOL (USA) Ltd.
• References: <a57hd0\$2kb\$1@smc.vnet.net> <200202250631.BAA09810@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```aes wrote:

> In article <a57hd0\$2kb\$1 at smc.vnet.net>,
>  steger at uni-greifswald.de (Thomas Steger) wrote:
>
> > I use Table[] together with FindRoot[] to repeatedly solve a system of
> > equations numerically. Now I would like to give the starting value for
> > the first calculation as prespecified while all subsequent starting
> > values should equal the n-1 th solution.
> >
> > Here is a simple example, where the starting value is fixed for all
> > calculations to follow.
> >
> > Clear[g1, g2]
> > g1 = a x + b y == c;
> > g2 = d x + e y == f;
> > Clear[a, b, c, d, e, f]
> > a = 0.5; b = 0.1; c = 2; d = 0.9; e = 1; f = .2;
> > Clear[a]
> > Table[FindRoot[{g1, g2}, {x, 4}, {y, -4}], {a, 0.5, 1, 0.1}]
>
> Me too.  More generally, I'd like to be able to use earlier ("already
> calculated"?) values in a table in calculating later values in the same table,
> e.g.
>
>    y = Table[ If[ k<2, k-1, a y[[k-1}] + b y[[k-2]] ], {k, 1, 5} ]
>
> but this doesn't work.
>
> [To handle things like this I resort to using a DO loop to calculate values of
> yTemp[k], then stuff these values into list y; but that's probably a naive --
> maybe even dumb? -- approach.]

You could do something like this:

y = {0,1,Block[{t1=0,t2=1,val},Sequence@@Table[val = a t1+b t2;t2 = t1;t1 =
val,{k,3,5}]}

There may be a more clever way of doing the assignments to avoid all the copies
but you get the idea.

Regards,

Sseziwa

```

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