Successive Over-relaxation Method (SOR). This method of solving a linear system of equations Ax = b derived by extrapolating the Gauss-Seidel method. This extrapolation takes the form of a weighted average between the previous iterate and the computed Gauss-Seidel iterate successively for each component.<\/p>\n

if \u00cf\u2030 = 1, the SOR method simplifies to the Gauss-Seidel method. A theorem due to Kahan (1958) shows that SOR fails to converge if \u00cf\u2030 is outside of the interval (0, 2). In general, it is not possible to compute in advance the value of \u00cf\u2030 that will maximize the rate of convergence of SOR.
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The successive over-relaxation method can be derived from the Gauss-Seidel method by introducing an extrapolation parameter omega. This method can converge faster than Gauss-Seidel by an order of magnitude <\/p>\n","protected":false},"excerpt":{"rendered":"

Successive Over-relaxation Method (SOR). This method of solving a linear system of equations Ax = b derived by extrapolating the Gauss-Seidel method. This extrapolation takes the form of a weighted average between the previous iterate and the computed Gauss-Seidel iterate successively for each component. if \u00cf\u2030 = 1, the SOR method simplifies to the Gauss-Seidel […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/32555"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=32555"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/32555\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=32555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=32555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=32555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}