Loop invariants in floating point algorithms |
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Authors: | K. -U. Jahn |
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Affiliation: | 1. Fachbereich Mathematik und Informatik, TH Leipzig, Karl-Liebknecht-Stra?e 132, 04275, Leipzig, Federal Republic of Germany
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Abstract: | It will be shown that by using directed roundings resp. enclosure sets for the exact values, the loop conditions and loop invariants of numerical algorithms can be generalized for computing in a discrete screen. On this way, in spite of rounding errors, it is possible to verify the received results. Thereby only inherent properties of the algorithms are used, which moreover guarantee that the loops terminate. |
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