{"id":7106,"date":"2021-05-26T07:37:24","date_gmt":"2021-05-26T11:37:24","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=7106"},"modified":"2021-05-26T09:24:27","modified_gmt":"2021-05-26T13:24:27","slug":"complexity-of-computing-the-eigenvalues-of-a-symmetric-matrix","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2021\/05\/26\/complexity-of-computing-the-eigenvalues-of-a-symmetric-matrix\/","title":{"rendered":"Complexity of Computing the Eigenvalues of a Symmetric Matrix"},"content":{"rendered":"<div class=\"content\"><!--introduction--><p>I am giving a five-minute talk today, May 26, at the virtual seminar on <a href=\"https:\/\/sites.google.com\/view\/cmc-seminar\">Complexity of Matrix Computations<\/a>.  Here are my slides.  Two new MATLAB functions, tred and imtql, instrumented to count flops, are available in <a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/symeig.m\">symeig.m<\/a>.<\/p><!--\/introduction--><h3>Contents<\/h3><div><ul><li><a href=\"#0a54e09a-3fba-4539-a323-b60dc7d2b6ce\">symeig_01<\/a><\/li><li><a href=\"#de43c040-9e09-43bc-8779-57390198f7a3\">symeig_02<\/a><\/li><li><a href=\"#91822e65-a968-4ce5-a9cc-8f1f2ecf1b01\">symeig_03<\/a><\/li><li><a href=\"#e5c569fa-25fa-4fa6-8c95-38fc444c06e3\">symeig_04<\/a><\/li><li><a href=\"#81c917a3-d32e-46ad-a88e-ad7590302b87\">symeig_05<\/a><\/li><li><a href=\"#4467bb9d-3369-4247-a932-8f8c943c14b1\">symeig_06<\/a><\/li><\/ul><\/div><h4>symeig_01<a name=\"0a54e09a-3fba-4539-a323-b60dc7d2b6ce\"><\/a><\/h4><pre class=\"codeinput\">    imshow(<span class=\"string\">'symeig_01.jpg'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_01.jpg\" alt=\"\"> <h4>symeig_02<a name=\"de43c040-9e09-43bc-8779-57390198f7a3\"><\/a><\/h4><pre class=\"codeinput\">    imshow(<span class=\"string\">'symeig_02.jpg'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_02.jpg\" alt=\"\"> <h4>symeig_03<a name=\"91822e65-a968-4ce5-a9cc-8f1f2ecf1b01\"><\/a><\/h4><pre class=\"codeinput\">    imshow(<span class=\"string\">'symeig_03.jpg'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_03.jpg\" alt=\"\"> <h4>symeig_04<a name=\"e5c569fa-25fa-4fa6-8c95-38fc444c06e3\"><\/a><\/h4><pre class=\"codeinput\">    imshow(<span class=\"string\">'symeig_04.jpg'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_04.jpg\" alt=\"\"> <h4>symeig_05<a name=\"81c917a3-d32e-46ad-a88e-ad7590302b87\"><\/a><\/h4><pre class=\"codeinput\">    imshow(<span class=\"string\">'symeig_05.jpg'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_05.jpg\" alt=\"\"> <h4>symeig_06<a name=\"4467bb9d-3369-4247-a932-8f8c943c14b1\"><\/a><\/h4><pre class=\"codeinput\">    imshow(<span class=\"string\">'symeig_06.jpg'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_06.jpg\" alt=\"\"> <script language=\"JavaScript\"> <!-- \r\n    function grabCode_a092c1a5e3ba488885248b14a02add6d() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='a092c1a5e3ba488885248b14a02add6d ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' a092c1a5e3ba488885248b14a02add6d';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2021 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_a092c1a5e3ba488885248b14a02add6d()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; R2021a<br><\/p><\/div><!--\r\na092c1a5e3ba488885248b14a02add6d ##### SOURCE BEGIN #####\r\n%% Computing Eigenvalues of Symmetric Matrices\r\n% I am giving a five-minute talk today, May 26, at the virtual seminar\r\n% on <https:\/\/sites.google.com\/view\/cmc-seminar Complexity of Matrix\r\n% Computations>.  Here are my slides.  Two new MATLAB functions,\r\n% tred and imtql, instrumented to count flops, are\r\n% available in <https:\/\/blogs.mathworks.com\/cleve\/files\/symeig.m symeig.m>.\r\n\r\n%% symeig_01\r\n%\r\n    imshow('symeig_01.jpg')\r\n\r\n%% symeig_02\r\n%\r\n    imshow('symeig_02.jpg')\r\n\r\n%% symeig_03\r\n%\r\n    imshow('symeig_03.jpg')\r\n\r\n%% symeig_04\r\n%\r\n    imshow('symeig_04.jpg')\r\n\r\n%% symeig_05\r\n%\r\n    imshow('symeig_05.jpg')\r\n\r\n%% symeig_06\r\n%\r\n    imshow('symeig_06.jpg')\r\n\r\n##### SOURCE END ##### a092c1a5e3ba488885248b14a02add6d\r\n-->","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img decoding=\"async\"  class=\"img-responsive\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/symeig_01.jpg\" onError=\"this.style.display ='none';\" \/><\/div><!--introduction--><p>I am giving a five-minute talk today, May 26, at the virtual seminar on <a href=\"https:\/\/sites.google.com\/view\/cmc-seminar\">Complexity of Matrix Computations<\/a>.  Here are my slides.  Two new MATLAB functions, tred and imtql, instrumented to count flops, are available in <a href=\"https:\/\/blogs.mathworks.com\/cleve\/files\/symeig.m\">symeig.m<\/a>.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/05\/26\/complexity-of-computing-the-eigenvalues-of-a-symmetric-matrix\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[11,13,4,6,16],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/7106"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=7106"}],"version-history":[{"count":6,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/7106\/revisions"}],"predecessor-version":[{"id":7126,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/7106\/revisions\/7126"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=7106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=7106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=7106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}