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.
Read more about this topic: Newton's Method
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“A beautiful woman is a practical poet, taming her savage mate, planting tenderness, hope and eloquence in all whom she approaches.”
—Ralph Waldo Emerson (1803–1882)