Summary
Techniques are emerging which automatically determine the effects of rounding error upon numerical methods of a certain type. Meaningful testing presupposes a reasonable basis for comparison. Typically, the error's effects upon a given method are compared either (i) with the effects of perturbing the computational problem or (ii) with the effects of rounding error upon a competing method. We show that the result of a type (ii) comparison often remains valid when the two methods are adapted for “sparse” data, though the comparison might be based upon a model of error propagation which requires that special care be taken. This observation sometimes provides a rationale for preferring comparisons (ii), since the results of type (i) comparisons may well not carry over to sparse data.
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Partially supported by NSF Grants GJ-42968 and MCS 76-13561 A01
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Miller, W. Roundoff analyses and sparse data. Numer. Math. 29, 37–43 (1977). https://doi.org/10.1007/BF01389311
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DOI: https://doi.org/10.1007/BF01389311