Practical Considerations
Newton's method is an extremely powerful technique—in general the convergence is quadratic: as the method converges on the root, the difference between the root and the approximation is squared (the number of accurate digits roughly doubles) at each step. However, there are some difficulties with the method.
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Famous quotes containing the word practical:
“Whether there be any such moral principles, wherein all men do agree, I appeal to any, who have been but moderately conversant in the history of mankind, and looked abroad beyond the smoke of their own chimneys. Where is that practical truth, that is universally received without doubt or question, as it must be, if innate?”
—John Locke (1632–1704)