“Error Propagation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Error Propagation

释义

Error Propagation

Given a Formula with an Absolute Error in of , the Absolute Error is . TheRelative Error is . If , then

(1)



			(2)

The definitions of Variance and Covariance then give

			(3)
			(4)
			(5)

(6)

and

are uncorrelated, then

(7)

Now consider addition of quantities with errors.For , and , so

(8)

For division of quantities with, and , so

(9)


			(10)

For exponentiation of quantities with

(11)

(12)

(13)

(14)

, then

(15)

For Logarithms of quantities with , , so

(16)

(17)

For multiplication with, and , so

(18)


			(19)

For Powers,with , , so

(20)

(21)

See also Absolute Error, Percentage Error, Relative Error

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 14, 1972.

Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill, pp. 58-64, 1969.

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