{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:17:39Z","timestamp":1776827859181,"version":"3.51.2"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"239","license":[{"start":{"date-parts":[[2002,11,20]],"date-time":"2002-11-20T00:00:00Z","timestamp":1037750400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, which allows the simultaneous approximation of the extreme solutions of the matrix equations\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper X plus upper A Superscript asterisk Baseline upper X Superscript negative 1 Baseline upper A equals upper Q\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>X<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>A<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:msup>\n                              <mml:mi>X<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>Q<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">X+A^* X^{-1}A=Q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper X minus upper A Superscript asterisk Baseline upper X Superscript negative 1 Baseline upper A equals upper Q\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>X<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>A<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:msup>\n                              <mml:mi>X<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>Q<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">X-A^*X^{-1}A=Q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The algorithm is based on the cyclic reduction method.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01368-0","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T15:46:54Z","timestamp":1032536814000},"page":"1189-1204","source":"Crossref","is-referenced-by-count":85,"title":["Efficient computation of the extreme solutions of \ud835\udc4b+\ud835\udc34*\ud835\udc4b\u207b\u00b9\ud835\udc34=\ud835\udc44 and \ud835\udc4b-\ud835\udc34*\ud835\udc4b\u207b\u00b9\ud835\udc34=\ud835\udc44"],"prefix":"10.1090","volume":"71","author":[{"given":"Beatrice","family":"Meini","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,11,20]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1080\/15326349708807433","article-title":"An invariant subspace approach in \ud835\udc40\/\ud835\udc3a\/1 and \ud835\udc3a\/\ud835\udc40\/1 type Markov chains","volume":"13","author":"Akar, Nail","year":"1997","journal-title":"Comm. 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