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As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno method depends only on the product of the dimensionality of the problem and the <jats:italic>logarithm<\/jats:italic> of its condition number.<\/jats:p>","DOI":"10.1007\/s10957-020-01805-8","type":"journal-article","created":{"date-parts":[[2021,1,9]],"date-time":"2021-01-09T09:34:52Z","timestamp":1610184892000},"page":"744-769","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["New Results on Superlinear Convergence of Classical Quasi-Newton Methods"],"prefix":"10.1007","volume":"188","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9656-8554","authenticated-orcid":false,"given":"Anton","family":"Rodomanov","sequence":"first","affiliation":[]},{"given":"Yurii","family":"Nesterov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,9]]},"reference":[{"key":"1805_CR1","doi-asserted-by":"crossref","unstructured":"Davidon, W.: Variable metric method for minimization. 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