Backward perturbation analysis for the matrix equation ATXA + BTY B = D
Abstract Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the si...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yang, Xing-dong [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematicae applicatae sinica / English series - Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 2002, 27(2011), 2 vom: 12. März, Seite 281-288 |
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| Übergeordnetes Werk: |
volume:27 ; year:2011 ; number:2 ; day:12 ; month:03 ; pages:281-288 |
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| DOI / URN: |
10.1007/s10255-011-0055-0 |
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OLC2109957530 |
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| 520 | |a Abstract Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples. | ||
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Abstract Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples. © Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011 |
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Abstract Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples. © Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011 |
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Abstract Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples. © Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2109957530</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502180540.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230502s2011 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10255-011-0055-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2109957530</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10255-011-0055-0-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.80$jAngewandte Mathematik</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Yang, Xing-dong</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Backward perturbation analysis for the matrix equation ATXA + BTY B = D</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Consider the linear matrix equation ATXA + BTY B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. 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