{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:38:13Z","timestamp":1776800293181,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"300","license":[{"start":{"date-parts":[[2016,8,31]],"date-time":"2016-08-31T00:00:00Z","timestamp":1472601600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zero-finding problems. The modified QZ algorithm computes the generalized eigenvalues of certain\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N times upper N\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N\\times N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    rank structured matrix pencils using\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper O left-parenthesis upper N squared right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">O(N^2)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    flops and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper O left-parenthesis upper N right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>O<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">O(N)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.\n                  <\/p>","DOI":"10.1090\/mcom\/3020","type":"journal-article","created":{"date-parts":[[2015,8,31]],"date-time":"2015-08-31T08:50:26Z","timestamp":1441011026000},"page":"1753-1774","source":"Crossref","is-referenced-by-count":8,"title":["Implicit QR for companion-like pencils"],"prefix":"10.1090","volume":"85","author":[{"given":"P.","family":"Boito","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Eidelman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Gemignani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,8,31]]},"reference":[{"issue":"2","key":"1","first-page":"101","article-title":"On matrices depending on parameters","volume":"26","author":"Arnol\u2032d, V. 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