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When multiplicative backward errors are small, the multiplicative perturbation theory for the singular value decomposition developed in the last decade can be applied to get high accuracy bounds on the errors of the computed singular values and vectors.<\/jats:p>","DOI":"10.1137\/s0895479803427005","type":"journal-article","created":{"date-parts":[[2004,6,15]],"date-time":"2004-06-15T14:24:20Z","timestamp":1087309460000},"page":"1021-1031","source":"Crossref","is-referenced-by-count":4,"title":["A Note on Multiplicative Backward Errors of Accurate SVD Algorithms"],"prefix":"10.1137","volume":"25","author":[{"given":"Froil\u00e1n M.","family":"Dopico","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julio","family":"Moro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"E. 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