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Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new algorithms have the potential to outperform, sometimes significantly, existing methods. This potential is demonstrated for several different types of PDEs.<\/jats:p>","DOI":"10.1007\/s00211-023-01372-w","type":"journal-article","created":{"date-parts":[[2023,9,20]],"date-time":"2023-09-20T13:01:56Z","timestamp":1695214916000},"page":"175-209","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Improved ParaDiag via low-rank updates and interpolation"],"prefix":"10.1007","volume":"155","author":[{"given":"Daniel","family":"Kressner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Massei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junli","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,9,20]]},"reference":[{"issue":"5","key":"1372_CR1","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0167-6911(02)00147-0","volume":"46","author":"AC Antoulas","year":"2002","unstructured":"Antoulas, A.C., Sorensen, D.C., Zhou, Y.: On the decay rate of Hankel singular values and related issues. 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