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Principles of Approximate Computations

Principles of Approximate Computations


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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: amount of the errors that would result by taking both numbers too small or both too large, with three decimals each, nor the direction of the errors if each were to be taken to the nearest 3d decimal, we have to determine in each the 4th decimal, giving 9.7468 - 2.2361 - 7.5107 Since the errors of the two quantities happen now to be in the same direction, the absolute error of the result cannot exceed 0.00005. Then the true difference lies between 7.5 106 and 7.5 108. Either of these limits would give for the answer with four exact figures, 7.511, the absolute error being then less than half a thousandth, and the relative error, therefore, (Art. 6) less than Ttetott loooo as required. Example 9. Compute the expression /3 ? V2, with a relative error less than ToW- Answer, 0.02804. 15. It hardly needs to be pointed out that if two numbers can be obtained, each with only a limited degree of approximation, the limit of the absolute error of the difference of the numbers will have to be taken equal to the sum of the limits of the errors of the numbers, unless it is known that their errors are in the same direction; in this case the larger of the two limits of error may be taken as the limit of error of the difference. For example, if the numbers 3.725 and 1.834 are each approximate within half a thousandth, but the direction of the errors not known, there will be an uncertainty of a thousandth in the difference, 1.891. If, however, we have the numbers 3.725 and 1.8342 each known to be too small by not more than half a unit of its lowest order, the error of the difference 1.8908 cannot exceed half a thousandth.MULTIPLICATION. 16. Problem 8. Two factors being proposed, whose values may be taken as accurately as we please, it is required to form their product so t...


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Product Details
  • ISBN-13: 9780217742801
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Edition: Abridged edition
  • Language: English
  • Returnable: N
  • Weight: 64 gr
  • ISBN-10: 0217742807
  • Publisher Date: 02 Feb 2012
  • Binding: Paperback
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Width: 189 mm


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