Camparison of Numerically Stability of Two Algorithms for the Calculation of Variance
In descriptive statistics, there are two computational algorithms for determining the variance S2, of a set of observations : Algorithm 1: S2= - , Algorithm 2: S2= , where . It is interesting to discuss, which of the above formulas is numerically more trustworthy in machine numbers sets. I thi...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
University of Tehran
2010-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_21083_6f77c247cc221e6cbf42374b5cb7f5f8.pdf |
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| Summary: | In descriptive statistics, there are two computational algorithms for determining the variance S2, of a set of observations :
Algorithm 1: S2= - ,
Algorithm 2: S2= ,
where . It is interesting to discuss, which of the above formulas is numerically more trustworthy in machine numbers sets. I this paper, based on total effect of rounding error, we prove that the second Algorithm is better than the first Algorithm. Numerical experiments show the efficiency of Algorithm 2. |
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| ISSN: | 1016-1104 2345-6914 |