Numerical operator calculus in higher dimensions
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Publication:4547728
DOI10.1073/pnas.112329799zbMath1008.65026OpenAlexW1980428773WikidataQ30453212 ScholiaQ30453212MaRDI QIDQ4547728
Martin J. Mohlenkamp, Gregory Beylkin
Publication date: 11 September 2002
Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)
Full work available at URL: http://www.pnas.org/content/vol99/issue16/#APPLIED_MATHEMATICS
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Cites Work