{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:19:41Z","timestamp":1787321981540,"version":"3.56.0"},"reference-count":29,"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>For $K + 1$ power series $a_0 ( z ), \\cdots ,a_k ( z )$, we present a new iterative, look-ahead algorithm for numerically computing Pad\u00e9\u2013Hermite systems and simultaneous Pad\u00e9 systems along a diagonal of the associated Pad\u00e9 tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are well conditioned. The operation and the stability of the algorithm is controlled by a single parameter $\\tau $ which serves as a threshold in deciding if the Sylvester matrices at a point are sufficiently well conditioned. We show that the algorithm is weakly stable and provide bounds for the error in the computed solutions as a function of $\\tau $. Experimental results are given which show that the bounds reflect the actual behavior of the error.<\/jats:p>\n                  <jats:p>The algorithm requires $\\mathcal{O} ( \\| n \\|^2 + s^3 \\| n \\| )$ operations to compute Pad\u00e9\u2013Hermite and simultaneous Pad\u00e9 systems of type $n = [ n_0 , \\cdots ,n_k ]$, where $\\| n \\| = n_0 + \\cdots + n_k $ and s is the largest step-size taken along the diagonal. An additional application of the algorithm is the stable inversion of striped and mosaic Sylvester matrices.<\/jats:p>","DOI":"10.1137\/s0895479894268695","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"268-297","source":"Crossref","is-referenced-by-count":12,"title":["Computation of Numerical Pad\u00e9\u2013Hermite and Simultaneous Pad\u00e9 Systems II: A Weakly Stable Algorithm"],"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","volume-title":"Pad\u00e9 approximants. 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