Re: Iterative application of FindRoot with adjusted started values

• To: mathgroup at smc.vnet.net
• Subject: [mg33007] Re: Iterative application of FindRoot with adjusted started values
• From: aes <siegman at stanford.edu>
• Date: Mon, 25 Feb 2002 01:31:25 -0500 (EST)
• Organization: Stanford University
• References: <a57hd0\$2kb\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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.]

```

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