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If division is much more costly than multiplication, it may be preferable to compute the inverse square root instead. Other methods are available to compute the square root digit by digit, or using Taylor series . Rational approximations of square roots may be calculated using continued fraction expansions .
Propagation of uncertainty. In statistics, propagation of uncertainty (or propagation of error) is the effect of variables ' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement ...
Use of Newton's method to compute square roots. Newton's method is one of many known methods of computing square roots. Given a positive number a, the problem of finding a number x such that x 2 = a is equivalent to finding a root of the function f(x) = x 2 − a. The Newton iteration defined by this function is given by
then. This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations). [1]
This picture shows clockwise from top left: An Arithmometer, a Comptometer, a Dalton adding machine, a Sundstrand, and an Odhner Arithmometer. A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a ...
Typical ten-inch (25 cm) student slide rule (Pickett N902-T simplex trig) A slide rule is a hand -operated mechanical calculator consisting of slidable rulers for evaluating mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry. It is one of the simplest analog computers.
The square root function maps rational numbers into algebraic numbers, the latter being a superset of the rational numbers). For all real numbers x , (see absolute value ). For all nonnegative real numbers x and y , and. The square root function is continuous for all nonnegative x, and differentiable for all positive x.
Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B ). Less frequently, the name square root may be used for any factorization of a ...