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docs/references/bib.bib

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@@ -2480,3 +2480,60 @@ @article{rump:2008b
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volume = {31},
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year = {2008},
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}
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@article{west:1979a,
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abstract = {A method of improved efficiency is given for updating the mean and variance of weighted sampled data when an additional data value is included in the set. Evidence is presented that the method is stable and at least as accurate as the best existing updating method.},
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author = {D H D West},
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doi = {10.1145/359146.359153},
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journal = {Communications of the ACM},
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keywords = {updating estimates, variance, standard deviation, mean, removing data},
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month = {sep},
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number = {9},
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pages = {532--535},
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title = {{Updating Mean and Variance Estimates: An Improved Method}},
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url = {https://doi.org/10.1145/359146.359153},
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volume = {22},
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year = {1979},
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}
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@article{chan:1979a,
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abstract = {Four algorithms for the numerical computation of the standard deviation of (unweighted) sampled data are analyzed. Two of the algorithms are well-known in the statistical and computational literature; the other two are new algorithms specifically intended for automatic computation. Our discussion is expository, with emphasis on reaching a suitable definition of “accuracy.” Each of the four algorithms is analyzed for the conditions under which it will be accurate. We conclude that all four algorithms will provide accurate answers for many problems, but two of the algorithms, one new, one old, are substantially more accurate on difficult problems than are the other two.},
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author = {Tony F. Chan and John Gregg Lewis},
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doi = {10.1145/359146.359152},
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journal = {Communications of the ACM},
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keywords = {least squares, rounding error analysis, mean, condition number, updating estimates, standard deviation, variance},
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month = {sep},
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number = {9},
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pages = {526--531},
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title = {{Computing Standard Deviations: Accuracy}},
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url = {https://doi.org/10.1145/359146.359152},
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volume = {2},
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year = {1979},
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}
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@inproceedings{chan:1982a,
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abstract = {A general formula is presented for computing the sample variances for a sample of size m + n given the means and variances for two subsamples of sizes m and n. This formula is used in the construction of a pairwise algorithm for computing the variance. Other applications are discussed as well, including the use of updating formulae in a parallel computing environment. We present numerical results and rounding error analyzes for several numerical schemes.},
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author = {Tony F Chan and Gene H Golub and Randall J LeVeque},
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booktitle = {COMPSTAT 1982 5th Symposium held at Toulouse 1982},
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doi = {10.1007/978-3-642-51461-6_3},
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keywords = {least squares, rounding error analysis, mean, condition number, updating estimates, standard deviation, variance},
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publisher = {Physica-Verlag HD},
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title = {{Updating Formulae and a Pairwise Algorithm for Computing Sample Variances}},
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url = {https://doi.org/10.1007/978-3-642-51461-6_3},
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year = {1982},
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}
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@article{youngs:1971a,
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abstract = {Sum and sum-of-product algorithms, some designed to minimize significance error, are compared and recommendations for usage are offered. A simplified method of rounding is presented and the benefit of using it demonstrated. Results are presented for the IBM 360 as well as the IBM 7040 computers with obvious application to some other machines.},
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author = {Edward A. Youngs and Elliot M. Cramer},
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doi = {10.1080/00401706.1971.10488826},
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journal = {Technometrics},
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keywords = {least squares, rounding error analysis, mean, condition number, updating estimates, standard deviation, variance},
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month = {},
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number = {3},
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pages = {657--665},
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title = {{Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms}},
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url = {https://amstat.tandfonline.com/doi/abs/10.1080/00401706.1971.10488826},
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volume = {13},
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year = {1971},
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}

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