{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:14:07Z","timestamp":1787382847475,"version":"3.56.0"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[1996,4]]},"abstract":"<jats:p>We present new formulae for the \u201cnear\u201d inverses of striped Sylvester and mosaic Sylvester matrices. The formulae assume computation over floating-point rather than exact arithmetic domains. The near inverses are expressed in terms of numerical Pad\u00e9\u2013Hermite systems and simultaneous Pad\u00e9 systems. These systems are approximants for the power series determined from the coefficients of the Sylvester matrices. The inverse formulae provide good estimates for the condition numbers of these matrices and serve as primary tools in a companion paper for the development of a fast, weakly stable algorithm for the computation of Pad\u00e9\u2013Hermite and simultaneous Pad\u00e9 systems and, thereby, also for the numerical inversion of striped and mosaic Sylvester matrices.<\/jats:p>","DOI":"10.1137\/s0895479894268683","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"248-267","source":"Crossref","is-referenced-by-count":8,"title":["Computation of Numerical Pad\u00e9\u2013Hermite and Simultaneous Pad\u00e9 Systems I: Near Inversion of Generalized Sylvester Matrices"],"prefix":"10.1137","volume":"17","author":[{"given":"Stan","family":"Cabay","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony R.","family":"Jones","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Labahn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","unstructured":"B. Beckermann, Ph.D. Thesis,  Zur Interpolation mit polynomialen Linearkombinationen beliebiger Funktionen, Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Hannover,  1988"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(92)90039-Z"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479892230031"},{"key":"R4","unstructured":"S. Cabay, A. Jones, G. Labahn,  A stable algorithm for multi-dimensional Pad\u00e9 systems and the inversion of generalized Sylvester matrices, Tech. Report, TR 94-07, Dept. Comp. Sci., Univ. Alberta,  1994"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894268695"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02145386"},{"key":"R7","unstructured":"S. Cabay, G. 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