We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equationsX<\/mml:mi>+<\/mml:mo>A<\/mml:mi>\u2217<\/mml:mo><\/mml:msup>X<\/mml:mi>\u2212<\/mml:mo>1<\/mml:mn><\/mml:mrow><\/mml:msup>A<\/mml:mi>=<\/mml:mo>Q<\/mml:mi><\/mml:mrow>X+A^*X^{-1}A=Q<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>andX<\/mml:mi>\u2212<\/mml:mo>A<\/mml:mi>\u2217<\/mml:mo><\/mml:msup>X<\/mml:mi>\u2212<\/mml:mo>1<\/mml:mn><\/mml:mrow><\/mml:msup>A<\/mml:mi>=<\/mml:mo>Q<\/mml:mi><\/mml:mrow>X-A^*X^{-1}A=Q<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>, whereQ<\/mml:mi>Q<\/mml:annotation><\/mml:semantics><\/mml:math><\/inline-formula>is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton\u2019s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation. Numerical results are reported to illustrate the convergence behaviour of various algorithms.<\/p>","DOI":"10.1090\/s0025-5718-99-01122-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"1589-1603","source":"Crossref","is-referenced-by-count":121,"title":["Iterative solution of two matrix equations"],"prefix":"10.1090","volume":"68","author":[{"given":"Chun-Hua","family":"Guo","sequence":"first","affiliation":[]},{"given":"Peter","family":"Lancaster","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1999,4,7]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0024-3795(90)90005-W","article-title":"Positive solutions to \ud835\udc4b=\ud835\udc34-\ud835\udc35\ud835\udc4b\u207b\u00b9\ud835\udc35*","volume":"134","author":"Anderson, W. 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