{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:54Z","timestamp":1760245074085},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"221","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Rutishauser, Gragg and Harrod and finally H.Y. Zha used the same class of chasing algorithms for transforming arrowhead matrices to tridiagonal form. Using a graphical theoretical approach, we propose a new chasing algorithm. Although this algorithm has the same sequential computational complexity and backward error properties as the old algorithms, it is better suited for a pipelined approach. The parallel algorithm for this new chasing method is described, with performance results on the Paragon and nCUBE. Comparison results between the old and the new algorithms are also presented.<\/p>","DOI":"10.1090\/s0025-5718-98-00895-3","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"221-235","source":"Crossref","is-referenced-by-count":9,"title":["A new parallel chasing algorithm for transforming arrowhead matrices to tridiagonal form"],"prefix":"10.1090","volume":"67","author":[{"given":"Suely","family":"Oliveira","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","unstructured":"Z. Chen, A parallel implementation of a chasing algorithm, tech. rep., Texas A&M University, 1996. project report."},{"key":"2","unstructured":"Z. Chen, Y. Deng, and S. Oliveira, A parallel implementation of a new chasing algorithm, tech. rep., Texas A&M University, 1996. manuscript."},{"key":"3","unstructured":"Y. Deng, Some applications of pipelining techniques in parallel scientific computing, Master\u2019s thesis, Texas A&M University, 1996."},{"key":"4","series-title":"Johns Hopkins Series in the Mathematical Sciences","isbn-type":"print","volume-title":"Matrix computations","volume":"3","author":"Golub, Gene H.","year":"1989","ISBN":"http:\/\/id.crossref.org\/isbn\/0801837723","edition":"2"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/BF01405565","article-title":"The numerically stable reconstruction of Jacobi matrices from spectral data","volume":"44","author":"Gragg, William B.","year":"1984","journal-title":"Numer. Math.","ISSN":"http:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"6","first-page":"219","article-title":"On Jacobi rotation patterns","author":"Rutishauser, H.","year":"1963"},{"key":"7","doi-asserted-by":"crossref","unstructured":"D. Stewart, A graph theoretical model of Givens rotations and its implications. 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Linear Algebra Appl.","ISSN":"http:\/\/id.crossref.org\/issn\/1070-5325","issn-type":"print"},{"issue":"1","key":"10","first-page":"49","article-title":"A two-way chasing scheme for reducing a symmetric arrowhead matrix to tridiagonal form","volume":"1","author":"Zha, Hong Yuan","year":"1992","journal-title":"J. Numer. 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