
06269367
j
2014b.00896
Neidinger, Richard D.
A classroom note: Newton's method doubles digit improvement.
Math. Comput. Educ. 48, No. 1, 1922 (2014).
2014
MATYC Journal, Old Bethpage, NY
EN
N50
Newton's method
iteration
approximation
quadratic convergence
From the text: The speed of convergence of Newton's rootfinding method is dramatically demonstrated in examples where the number of accurate digits doubles with each iteration. But what is meant by this common description of the formal concept called quadratic convergence? If the approximation and exact value round to the same digit, we call it an accurate digit; but where do you start counting? We could start at the first nonzero, counting accurate significant digits. One of my students counted accurate digits from the decimal point. Both are wrong; our digit counts may not double. The improvement, the number of newly accurate digits in each approximation, will roughly double.