{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:12Z","timestamp":1787323212067,"version":"3.56.0"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[1996,7]]},"abstract":"<jats:p>In this paper, we discuss the problem of constructing a $2n \\times 2n$ Jacobi matrix $J_{2n} $ such that its eigenvalues are given distinct values $\\lambda _1 ,\\lambda _2 , \\cdots ,\\lambda _{2n} $ and its leading $n \\times n$ principal submatrix is a given $n \\times n$ Jacobi matrix $J_n $. We give some sufficient and necessary conditions for the solubility of the problem and propose a new fast algorithm for solving this problem. We also present some numerical results.<\/jats:p>","DOI":"10.1137\/s089547989122065x","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"632-639","source":"Crossref","is-referenced-by-count":29,"title":["On the Jacobi Matrix Inverse Eigenvalue Problem with Mixed Given Data"],"prefix":"10.1137","volume":"17","author":[{"given":"Shu-Fang","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/3\/4\/010"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(84)90069-7"},{"key":"R3","unstructured":"H. Dai,  On the Construction of a Jacobi Matrix From Its Spectrum and a Submatrix, Tech. report, NHJB-89-5760, Nanjing Aeronautical Institute, P. R. China,  1989"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-1178-0"},{"key":"R5","volume-title":"Matrix computations","author":"Golub Gene H.","year":"1983"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(79)90124-1"},{"key":"R7","volume-title":"The symmetric eigenvalue problem","author":"Parlett Beresford N.","year":"1980"},{"key":"R8","unstructured":"Q. J. Shen,  A new fast algorithm of reducing a symmetric bordered diagonal matrix to tridiagonal form,  Proceedings of the 1991 Tianjin Conference on Computational Mathematics, Tianjin, China,  521\u2013523"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S089547989122065X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:48:16Z","timestamp":1787320096000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S089547989122065X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["10.1137\/S089547989122065X"],"URL":"https:\/\/doi.org\/10.1137\/s089547989122065x","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}