Positive extension and completion problems for a class of structured matrices
A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions.
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| Published in | Linear & multilinear algebra Vol. 48; no. 3; pp. 189 - 235 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Gordon and Breach Science Publishers
01.03.2001
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-1087 1563-5139 |
| DOI | 10.1080/03081080108818669 |
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| Abstract | A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions. |
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| AbstractList | A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under certain positivity constraints. The extension problem is reduced to a standard interpolation problem for Schur matrix valued functions. |
| Author | Bolotnikov, V. Rodman, L. |
| Author_xml | – sequence: 1 givenname: V. surname: Bolotnikov fullname: Bolotnikov, V. organization: Department of Mathematics , The College of William and Mary – sequence: 2 givenname: L. surname: Rodman fullname: Rodman, L. email: lxrodman@math.wm.edu organization: Department of Mathematics , The College of William and Mary |
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| Cites_doi | 10.1016/0024-3795(81)90215-9 10.1016/0005-1098(88)90095-7 10.1016/S0024-3795(97)00048-7 10.1007/BF01193458 10.1002/mana.19891440118 10.1016/0005-1098(83)90103-6 10.1007/BF01261203 10.1137/S0895479895296471 10.1016/0022-247X(79)90124-0 10.1109/TASSP.1976.1162795 10.1007/978-94-009-0059-2 10.1007/BF01193460 10.1007/BF01691075 10.1007/BF01194989 10.1137/1037082 10.1080/03081089008817973 10.1017/CBO9780511569678.010 |
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| Copyright | Copyright Taylor & Francis Group, LLC 2001 |
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| References | Dym H. (CIT0014) 1989; 71 Gohberg I. (CIT0024) 1993; 63 CIT0030 CIT0010 Foias C. (CIT0022) 1998; 100 Bolotnikov (CIT0008) 1990; 45 CIT0031 CIT0033 Heinig G. (CIT0026) 1984; 13 Constantinescu T. (CIT0011) 1996; 82 Alpay D. (CIT0001) 1998; 6 CIT0016 Foias C. (CIT0021) 1990; 44 Gohberg I. (CIT0025) 1989; 22 CIT0015 CIT0018 CIT0017 CIT0019 Alpay D. (CIT0005) 1997; 23 Ball J. A. (CIT0007) 1990; 45 CIT0020 CIT0023 Woerdeman H. J. (CIT0036) 1989 Bakonyi M. (CIT0006) 1992; 261 Rosenblum M. (CIT0034) 1985 CIT0003 CIT0002 Dubovoj V. K. (CIT0012) 1982; 37 CIT0027 Johnson C. R. (CIT0028) 1988; 35 Sakhnovich L. A. (CIT0035) 1997 Dubovoj V.K. (CIT0013) 1992; 129 CIT0029 Marshall A. W. (CIT0032) 1979 Alpay D. (CIT0004) 1997; 23 CIT0009 |
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| Snippet | A class of matrices, defined by a displacement rank property, is introduced. Completion and extension problems are studied for matrices in this class, under... |
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| SubjectTerms | AMS Subject Classification: 15A45, 15A48 Generalized Toeplitz Positive completions Positive extensions Schur interpolation problem Structured matrices |
| Title | Positive extension and completion problems for a class of structured matrices |
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