How do we start from approximating a root using this technique? I know of two, viz - a table of x vs f(x), and see where f(x) changes sign - plot a graph, and see where the graph cuts the x axis But both these methods are unsatisfactory and laborious, and for large equations or transcendental equations, the calculation itself makes it prone to errors creeping in. Is there something more efficient?
2026-04-09 12:04:27.1775736267
Newton Raphson Method: approximating root
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I don't think there's any technique that's much better than the ones you mentioned. Calculating a table of values isn't really laborious if you're using a computer (which is what you'll be doing in any practical situation).
There are theorems that tell us that Newton's method will converge from any starting point under certain conditions, but these conditions are typically difficult to check, so this doesn't help very much.
Sorry -- no silver bullet (as far as I know).