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The piecewise linear equation system <jats:inline-formula><jats:alternatives><jats:tex-math>$$z-A\\vert z\\vert = b$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>z<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mi>A<\/mml:mi>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:mi>z<\/mml:mi>\n                    <mml:mo>|<\/mml:mo>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mi>b<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is called an <jats:italic>absolute value equation<\/jats:italic>. In this note we consider two solvers for uniquely solvable instances of the latter problem, one direct, one semi-iterative. We slightly extend the existing correctness, resp. convergence, results for the latter algorithms and provide numerical tests.<\/jats:p>","DOI":"10.1007\/s11590-021-01837-7","type":"journal-article","created":{"date-parts":[[2021,12,25]],"date-time":"2021-12-25T13:02:36Z","timestamp":1640437356000},"page":"1663-1673","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Convergence results for some piecewise linear solvers"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4272-2493","authenticated-orcid":false,"given":"Manuel","family":"Radons","sequence":"first","affiliation":[]},{"given":"Siegfried M.","family":"Rump","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,25]]},"reference":[{"issue":"1","key":"1837_CR1","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1214\/aoms\/1177729698","volume":"22","author":"MS Bartlett","year":"1951","unstructured":"Bartlett, M.S.: An inverse matrix adjustment arising in discriminant analysis. 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