Rough Estimation
Many of the methods for calculating square roots of a positive real number S require an initial seed value. If the initial value is too far from the actual square root, the calculation will be slowed down. It is therefore useful to have a rough estimate, which may be very inaccurate but easy to calculate. If S ≥ 1, let D be the number of digits to the left of the decimal point. If S < 1, let D be the negative of the number of zeros to the immediate right of the decimal point. Then the rough estimation is this:
- If D is odd, D = 2n + 1, then use
- If D is even, D = 2n + 2, then use
Two and six are used because they approximate the geometric means of the lowest and highest possible values with the given number of digits: and
When working in the binary numeral system (as computers do internally), an alternative method is to use (here D is the number of binary digits).
Read more about this topic: Methods Of Computing Square Roots
Famous quotes containing the words rough and/or estimation:
“Evil can be got very easily and exists in quantity: the road to her is very smooth, and she lives near by. But between us and virtue the gods have placed the sweat of our brows; the road to her is long and steep, and it is rough at first; but when a man has reached the top, then she is easy to attain, although before she was hard.”
—Hesiod (c. 8th century B.C.)
“No man ever stood lower in my estimation for having a patch in his clothes; yet I am sure that there is greater anxiety, commonly, to have fashionable, or at least clean and unpatched clothes, than to have a sound conscience.”
—Henry David Thoreau (18171862)