{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:38:16Z","timestamp":1759091896202},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T00:00:00Z","timestamp":1340064000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2012,10]]},"DOI":"10.1007\/s11075-012-9606-6","type":"journal-article","created":{"date-parts":[[2012,6,18]],"date-time":"2012-06-18T07:52:03Z","timestamp":1340005923000},"page":"243-260","source":"Crossref","is-referenced-by-count":5,"title":["Error analysis for matrix eigenvalue algorithm based on the discrete hungry Toda equation"],"prefix":"10.1007","volume":"61","author":[{"given":"Akiko","family":"Fukuda","sequence":"first","affiliation":[]},{"given":"Yusaku","family":"Yamamoto","sequence":"additional","affiliation":[]},{"given":"Masashi","family":"Iwasaki","sequence":"additional","affiliation":[]},{"given":"Emiko","family":"Ishiwata","sequence":"additional","affiliation":[]},{"given":"Yoshimasa","family":"Nakamura","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,19]]},"reference":[{"key":"9606_CR1","volume-title":"Total Positivity and Its Applications, Math. Appl., vol. 359","year":"1996","unstructured":"Gasca, M., Micchelli, C.A. (eds.): Total Positivity and Its Applications, Math. Appl., vol. 359. Kluwer Academic, Dordrecht (1996)"},{"key":"9606_CR2","series-title":"Johns Hopkins Studies in the Mathematical Sciences","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"key":"9606_CR3","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s002110050024","volume":"25","author":"KV Fernando","year":"1994","unstructured":"Fernando, K.V., Parlett, B.N.: Accurate singular values and differential qd algorithms. Numer. Math. 25, 191\u2013229 (1994)","journal-title":"Numer. Math."},{"key":"9606_CR4","author":"A Fukuda","year":"2012","unstructured":"Fukuda, A., Ishiwata, E., Iwasaki, M., Yamamoto, Y., Nakamura, Y.: Integrable discrete hungry systems and their related matrix eigenvalues. Ann. Mat. Pura Appl. (2012). doi: 10.1007\/s10231-011-0231-0","journal-title":"Ann. Mat. Pura Appl."},{"key":"9606_CR5","author":"A Fukuda","year":"2012","unstructured":"Fukuda, A., Yamamoto, Y., Iwasaki, M., Ishiwata, E., Nakamura, Y.: On a shifted LR transformation derived from the discrete hungry Toda equation. Monat. Math. (2012). doi: 10.1007\/s00605-012-0404-y","journal-title":"Monat. Math."},{"key":"9606_CR6","volume-title":"Accuracy and Stability of Numerical Algorithms","author":"NJ Higham","year":"1996","unstructured":"Higham, N.J.: Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia (1996)"},{"key":"9606_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S0895479803438225","volume":"27","author":"P Koev","year":"2005","unstructured":"Koev, P.: Accurate eigenvalues and SVDs of totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 27, 1\u201323 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9606_CR8","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1017\/S0962492900002580","volume":"4","author":"BN Parlett","year":"1995","unstructured":"Parlett, B.N.: The new qd algorithms. Acta Numer. 4, 459\u2013491 (1995)","journal-title":"Acta Numer."},{"key":"9606_CR9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511691713","volume-title":"Totally Positive Matrices","author":"A Pinkus","year":"2009","unstructured":"Pinkus, A.: Totally Positive Matrices. Cambridge University Press, New York (2009)"},{"key":"9606_CR10","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1007\/BF01899329","volume":"5","author":"H Rutishauser","year":"1954","unstructured":"Rutishauser, H.: Ein infinitesimales Analogon zum Quotienten-Differenzen-Algorithmus. Arch. Math. 5, 132\u2013137 (1954) (in German)","journal-title":"Arch. Math."},{"key":"9606_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3468-5","volume-title":"Lectures on Numerical Mathematics","author":"H Rutishauser","year":"1990","unstructured":"Rutishauser, H.: Lectures on Numerical Mathematics. Birkh\u00e4user, Boston (1990)"},{"key":"9606_CR12","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1088\/0266-5611\/15\/6\/314","volume":"15","author":"T Tokihiro","year":"1999","unstructured":"Tokihiro, T., Nagai, A., Satsuma, J.: Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization. Inverse Probl. 15, 1639\u20131662 (1999)","journal-title":"Inverse Probl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9606-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-012-9606-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9606-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:18Z","timestamp":1559351298000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-012-9606-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,19]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["9606"],"URL":"https:\/\/doi.org\/10.1007\/s11075-012-9606-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,19]]}}}