> *if you need n-1 for the first iteration how do you compute it?*

zckumling said "I have a reasonable first guess x(n)".

That's all which is needed. It does not have to be a "good" guess, just not too very far wrong. For a tube circuit, "0.5 times supply" or "+150V" will get the iteration started.

How would you find the square-root of 7? Without a calculator, slide-rule, or framing-square?

Guess, check, note high/low, guess again. Repeat until close-enuff.

7 is a small number so its SR is probably a small number?

2^2= 4, too low.

3^2= 9, too high. But closer than 4.

Be stupid. Split the difference. 2.5^2= 6.25.

Pick a number closer to 3 than to 2.

2.6^2= 6.76. Getting closer.

2.7^2= 7.29. Close but over-shot.

2.65^2= 7.0225, which may be close enough for any practical purpose.

If more accuracy is wanted, try 2.645^2= 6.996.. which is very close.

Six easy steps found square-root of 7 within 0.06%.

zckumling wants a result equal to his successive guess.

In a tube circuit where the answer is really 200V, a first-guess of "150" would give a result of 180, wrong. A next-guess of 180 might give 190. Guessing 190 might give 199. And in tube-work, 199 is exactly equal to 200 because all self-biased tube-work is 10% precision at best. Even with a pretty-bad starting-guess like 50V, it should take very few iterations to get a result with better "accuracy" than the tubes we use.

> *it doesn't converge*

I can think-about math, but I can't DO math. So I don't know.

However triodes are not that non-linear. It should converge within 10% in very few steps; else you have lost a negative-sign or multiplied where you should divide. I suggest you print the first half-dozen iterations for a "known" circuit, and see if the numbers go toward the known answer or head off in the wrong direction. The size and direction of deviation may suggest where your formula is incorrect.

ARON: this could perhaps be moved to Stimulation section. zckumling is doing simulation, just not with a for-purpose simulator. Some of the sim-wizards there may know where zckumling has gone wrong.