A Newton-squaring algorithm for computing the negative invariant subspace of a matrix
By combining Newton's method for the matrix sign function with a squaring procedure, a basis for the negative invariant subspace of a matrix can be computed efficiently. The algorithm presented is a variant of multiplication-rich schemes for computing the matrix sign function, such as the well-...
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| Veröffentlicht in: | IEEE transactions on automatic control 1993-08, Vol.38 (8), p.1284-1289 |
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| container_end_page | 1289 |
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| container_issue | 8 |
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| container_title | IEEE transactions on automatic control |
| container_volume | 38 |
| creator | Kenney, C.S. Laub, A.J. Papadopoulos, P.M. |
| description | By combining Newton's method for the matrix sign function with a squaring procedure, a basis for the negative invariant subspace of a matrix can be computed efficiently. The algorithm presented is a variant of multiplication-rich schemes for computing the matrix sign function, such as the well-known inversion-free Schulz method, which requires two matrix multiplications per step. However, by avoiding a complete computation of the matrix sign and instead concentrating only on the negative invariant subspace, the final Newton steps can be replaced by steps which require only one matrix squaring each. This efficiency is attained without sacrificing the quadratic convergence of Newton's method.< > |
| doi_str_mv | 10.1109/9.233171 |
| format | Article |
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The algorithm presented is a variant of multiplication-rich schemes for computing the matrix sign function, such as the well-known inversion-free Schulz method, which requires two matrix multiplications per step. However, by avoiding a complete computation of the matrix sign and instead concentrating only on the negative invariant subspace, the final Newton steps can be replaced by steps which require only one matrix squaring each. This efficiency is attained without sacrificing the quadratic convergence of Newton's method.< ></description><subject>Applied sciences</subject><subject>Automatic control</subject><subject>Computer science; control theory; systems</subject><subject>Control systems</subject><subject>Control theory. Systems</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Exact sciences and technology</subject><subject>Feedback</subject><subject>MATLAB</subject><subject>Optimal control</subject><subject>Regulators</subject><subject>Riccati equations</subject><subject>Software algorithms</subject><subject>System theory</subject><subject>Weight control</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><recordid>eNqNkM1LAzEQxYMoWKvg2VMOIl62JpvsNjkW8QuKXux5mWSTNrJfTbJV_3u3bOnZywwz8-O94SF0TcmMUiIf5CxljM7pCZrQLBNJmqXsFE0IoSKRqcjP0UUIX8OYc04naLXA7-Y7tk0Stj1416wxVOvWu7ipsW091m3d9XG_jxuDG7OG6HYGu2Y30NBEHHoVOtAGtxYDriF693OJzixUwVwd-hStnp8-H1-T5cfL2-NimWjGspjw1BKrSgJcDbUsTWlzsIqmUhJG1ZxJKBUXJKcqB20zCYpLShkXUpTzTLMpuht1O99uexNiUbugTVVBY9o-FKmQkpOc_wPkgtFcDOD9CGrfhuCNLTrvavC_BSXFPuBCFmPAA3p70ISgobIeGu3CkR-epBnZW9-MmDPGHK8HjT8kj4MI</recordid><startdate>19930801</startdate><enddate>19930801</enddate><creator>Kenney, C.S.</creator><creator>Laub, A.J.</creator><creator>Papadopoulos, P.M.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>H8D</scope></search><sort><creationdate>19930801</creationdate><title>A Newton-squaring algorithm for computing the negative invariant subspace of a matrix</title><author>Kenney, C.S. ; Laub, A.J. ; Papadopoulos, P.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-42f0fbd0a4bbd0ddedf6afb1299031b739adb48061b6acf59ab491134898d75c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><topic>Applied sciences</topic><topic>Automatic control</topic><topic>Computer science; control theory; systems</topic><topic>Control systems</topic><topic>Control theory. Systems</topic><topic>Eigenvalues and eigenfunctions</topic><topic>Exact sciences and technology</topic><topic>Feedback</topic><topic>MATLAB</topic><topic>Optimal control</topic><topic>Regulators</topic><topic>Riccati equations</topic><topic>Software algorithms</topic><topic>System theory</topic><topic>Weight control</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kenney, C.S.</creatorcontrib><creatorcontrib>Laub, A.J.</creatorcontrib><creatorcontrib>Papadopoulos, P.M.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Aerospace Database</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kenney, C.S.</au><au>Laub, A.J.</au><au>Papadopoulos, P.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Newton-squaring algorithm for computing the negative invariant subspace of a matrix</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>1993-08-01</date><risdate>1993</risdate><volume>38</volume><issue>8</issue><spage>1284</spage><epage>1289</epage><pages>1284-1289</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>By combining Newton's method for the matrix sign function with a squaring procedure, a basis for the negative invariant subspace of a matrix can be computed efficiently. The algorithm presented is a variant of multiplication-rich schemes for computing the matrix sign function, such as the well-known inversion-free Schulz method, which requires two matrix multiplications per step. However, by avoiding a complete computation of the matrix sign and instead concentrating only on the negative invariant subspace, the final Newton steps can be replaced by steps which require only one matrix squaring each. This efficiency is attained without sacrificing the quadratic convergence of Newton's method.< ></abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/9.233171</doi><tpages>6</tpages></addata></record> |
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| ispartof | IEEE transactions on automatic control, 1993-08, Vol.38 (8), p.1284-1289 |
| issn | 0018-9286 1558-2523 |
| language | eng |
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| source | IEEE Xplore |
| subjects | Applied sciences Automatic control Computer science control theory systems Control systems Control theory. Systems Eigenvalues and eigenfunctions Exact sciences and technology Feedback MATLAB Optimal control Regulators Riccati equations Software algorithms System theory Weight control |
| title | A Newton-squaring algorithm for computing the negative invariant subspace of a matrix |
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