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Math. Softw."],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:p>\n            In this article, we propose a numerical algorithm for efficient and robust solution of a sequence of shifted Hessenberg linear systems. In particular, we show how the frequency response \ud835\udca2(\u03c3) =\n            <jats:italic>d<\/jats:italic>\n            -\n            <jats:italic>C<\/jats:italic>\n            (\n            <jats:italic>A<\/jats:italic>\n            -\u03c3 I)\n            <jats:sup>-1<\/jats:sup>\n            <jats:italic>b<\/jats:italic>\n            in the single input case can be computed more efficiently than with other state-of-the-art methods. We also provide a backward stability analysis of the proposed algorithm.\n          <\/jats:p>","DOI":"10.1145\/2049673.2049676","type":"journal-article","created":{"date-parts":[[2012,1,3]],"date-time":"2012-01-03T15:59:14Z","timestamp":1325606354000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["A note on shifted Hessenberg systems and frequency response computation"],"prefix":"10.1145","volume":"38","author":[{"given":"Christopher","family":"Beattie","sequence":"first","affiliation":[{"name":"Virginia Polytechnic Institute and State University, Blacksburg, VA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zlatko","family":"Drma\u010d","sequence":"additional","affiliation":[{"name":"University of Zagreb, Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Serkan","family":"Gugercin","sequence":"additional","affiliation":[{"name":"Virginia Polytechnic Institute and State University, Blacksburg, VA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,1,5]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Ammar G. and Gragg W. 1994. 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