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Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
Truncation of positive real numbers can be done using the floor function.Given a number + to be truncated and , the number of elements to be kept behind the decimal point, the truncated value of x is
One method, more obscure than most, is to alternate direction when rounding a number with 0.5 fractional part. All others are rounded to the closest integer. Whenever the fractional part is 0.5, alternate rounding up or down: for the first occurrence of a 0.5 fractional part, round up, for the second occurrence, round down, and so on.
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
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Truncation can be applied to any probability distribution.This will usually lead to a new distribution, not one within the same family. Thus, if a random variable X has F(x) as its distribution function, the new random variable Y defined as having the distribution of X truncated to the semi-open interval (a, b] has the distribution function
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Suppose we have a continuous differential equation ′ = (,), =, and we wish to compute an approximation of the true solution () at discrete time steps ,, …,.For simplicity, assume the time steps are equally spaced: