[원서][수치해석학입문] numerical mathematics and computing(6 e) - E. Ward Chene…
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Suppose that α and β are two numbers, of which one is regarded as an approximation to the other. The error of β as an approximation to α is α −β; that is, the error equals the exact value minus the approximate value. The absolute error of β as an approximation to α is|α−β|.Therelativeerrorof β asanapproximationto α is|α−β|/|α|.Noticethatin computing the absolute error, the roles of α and β are the same, whereas in computing the relative error, it is essential to distinguish one of the two numbers as correct. (Observe that the relative error is undefined in the case α =0.) For practical reasons, the relative error is usually more meaningful than the absolute error. For example, if α1 =1.333, β1 =1.334, and α2 = 0.001, β2 = 0.002, then the absolute error of βi as an approximation to αi is the same in both cases—namely, 10−3. However, the relative errors are 3 4 ×10−3 and 1,respectively. The relative error clearly indicates that β1 is a good approximation to α1 but that β2 is a poor approximation to α2. In summary, we have absolute error =|exact value−approximate value| relative error = |exact value−approximate value| |exact value| Heretheexactvalueisthetruevalue.Ausefulwaytoexpresstheabsoluteerrorandrelative error is to drop the absolute values and write (relative error)(exact value) = exact value−approximate value approximate value = (exact value)[1+(relative error)] Sotherelativeerrorisrelatedtotheapproximatevalueratherthantotheexactvaluebecause
- E. Ward Cheney, David R. Kincaid
Thomson
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[원서][수치해석학입문] numerical mathematics and computing(6 ed)
Sixth Edition
[원서][수치해석학입문] numerical mathematics and computing(6 e) - E. Ward Cheney, David R. Kincaid
Numerical mathematics and computing
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[원서][수치해석학입문] Numerical mathematics and computing Sixth Edition - E. Ward Cheney, David R. Kincaid Thomson
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