An Outline of the Problems

Heinz Rutishauser

Chapter Chapter 1 in Lectures on Numerical Mathematics, 1990, pp 1-9 from Springer

Abstract: Abstract The object of numerical mathematics is to devise a numerical approach for solving mathematically defined problems, i.e., to exhibit a detailed description of the computational process which eventually produces the solution of the problem in numerical form (for example, a numerical table). In so doing, one must, of course, be cognizant of the fact that a numerical computation almost never is entirely exact, but is more or less perturbed by the so-called rounding errors. The computing process, indeed, is executed in finite arithmetic, for example in floatingpoint arithmetic (number representation: z = a x 10 b ), where only a finite number of digits are at disposal both for the mantissa a and for the exponent b.

Keywords: Computational Process; Interval Analysis; Interval Arithmetic; Posteriori Error Estimate; Formal Algorithm (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-1-4612-3468-5_1

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