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Computer Arithmetic and Fundamental Concepts of Computation

In: A Graduate Introduction to Numerical Methods

Author

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  • Robert M. Corless

    (University of Western Ontario, Applied Mathematics)

  • Nicolas Fillion

    (University of Western Ontario, Applied Mathematics)

Abstract

This chapter introduces the main concepts of error analysis used in this book. The chapter defines reference problems and modified problems and notation to distinguish them. Two kinds of modified problems are shown to be particularly important in numerical analysis, namely, engineered and reverse-engineered problems. The reader is introduced to three concepts of error: (forward error, backward error, and residual), to the concept of conditioning, and to residual-based backward error analysis—which is the method favored in this book. We define numerical properties of algorithms, including stability and cost. Finally, we apply those concepts to floating-point arithmetic. ⊲

Suggested Citation

  • Robert M. Corless & Nicolas Fillion, 2013. "Computer Arithmetic and Fundamental Concepts of Computation," Springer Books, in: A Graduate Introduction to Numerical Methods, edition 127, chapter 0, pages 7-41, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8453-0_1
    DOI: 10.1007/978-1-4614-8453-0_1
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