NDLI: APPENDIX Computer Arithmetic Error Control

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APPENDIX Computer Arithmetic Error Control

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Abstract	In mathematical computations on a computer, errors are introduced into the solutions. These errors are brought into a calculation in three ways: 1. Error is present at the outset in the original data-inherent error 2. Error results from replacing an infinite process by a finite one-truncation error, i.e., representing a function by the first few terms of a Taylor series expansion 3. Error arises as a result of the finite precision of the numbers that can be represented in a computer-round-off error. Each of these errors is unavoidable in a calculation, and hence the problem is not to prevent their occurrence, but rather to control their magnitude. The control of inherent error is not within the scope of this text, and the truncation errors pertaining to specific methods are discussed in the appropriate chapters. This section outlines computer arithmetic and how it influences round-off errors. COMPUTER NUMBER SYSTEM The mathematician or engineer, in seeking a solution to a problem, assumes that all calculations will be performed within the system of real numbers,!7{. In!7{, the interval between any two real numbers contains infinitely many real numbers.!7 { does not exist in a computer because there are only a finite amount
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Subject Keyword	Appendix Computer Arithmetic Error Control Real Number Computer-round-off Error Finite One-truncation Error Taylor Series Expansion Round-off Error First Term Finite Precision Finite Amount Infinite Process Inherent Error Many Real Number Original Data-inherent Error Specific Method Appropriate Chapter Truncation Error Mathematical Computation Computer Number System Error Result
Content Type	Text

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