Four Variational Formulations of the Contraharmonic Mean of Operators

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Previous article Next article Four Variational Formulations of the Contraharmonic Mean of OperatorsW. L. Green and T. D. MorleyW. L. Green and T. D. Morleyhttps://doi.org/10.1137/0608055PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract The authors establish four variational expressions, each related to the parallel sum, for the contraharmonic mean of two positive operators or matrices.[1] W. N. Anderson and , R. J. Duffin, Series and parallel addition of matrices, J. Math. Anal. Appl., 26 (1969), 576–594 10.1016/0022-247X(69)90200-5 39:3904 0177.04904 CrossrefISIGoogle Scholar[2] W. N. Anderson, , M. E. Mays and , G. E. Trapp, The contraharmonic mean of HSD matrices and electrical networks, Proc. 27th Midwest Symposium on Circuits and Systems, 1984, 665–668, June Google Scholar[3] W. N. Anderson, , M. E. Mays, , T. D. Morley and , G. E. Trapp, The contraharmonic mean of HSD matrices, SIAM J. Algebraic Discrete Methods, 8 (1987), 674–682 89b:47030 0641.15009 LinkISIGoogle Scholar[4] W. N. Anderson and , G. E. Trapp, Shorted operators. II, SIAM J. Appl. Math., 28 (1975), 60–71 10.1137/0128007 50:9417 0295.47032 LinkISIGoogle Scholar[5] T. Ando, Topics on operator inequalities, Division of Applied Mathematics, Research Institute of Applied Electricity, Hokkaido University, Sapporo, 1978ii+44, Japan 58:2451 0696.47001 Google Scholar[6] P. A. Fillmore and , J. P. Williams, On operator ranges, Advances in Math., 7 (1971), 254–281 45:2518 0224.47009 CrossrefISIGoogle Scholar[7] William L. Green and , T. D. Morley, Operator means, fixed points, and the norm convergence of monotone approximants, Math. Scand., 60 (1987), 202–218 88k:47018 0663.47017 CrossrefISIGoogle Scholar[8] T. D. Morley, Parallel summation, Maxwell's principle and the infimum of projections, J. Math. Anal. Appl., 70 (1979), 33–41 10.1016/0022-247X(79)90073-8 80g:94075 0456.47021 CrossrefISIGoogle Scholar[9] Sujit Kumar Mitra and , Madan Lal Puri, On parallel sum and difference of matrices, J. Math. Anal. Appl., 44 (1973), 92–97 10.1016/0022-247X(73)90027-9 48:3989 0271.15008 CrossrefISIGoogle Scholar[10] George E. Trapp, Hermitian semidefinite matrix means and related matrix inequalities—an introduction, Linear and Multilinear Algebra, 16 (1984), 113–123 86f:15009 0548.15013 CrossrefGoogle ScholarKeywordscontraharmonic meanparallel sumpositive operatorpositive semi-definite matrixvariational formulation Previous article Next article FiguresRelatedReferencesCited byDetails The Contraharmonic Mean of HSD MatricesWilliam N. Anderson, Jr., Michael E. Mays, Thomas D. Morley, and George E. Trapp17 July 2006 | SIAM Journal on Algebraic Discrete Methods, Vol. 8, No. 4AbstractPDF (766 KB) Volume 8, Issue 4| 1987SIAM Journal on Algebraic Discrete Methods History Submitted:29 December 1986Accepted:21 April 1987Published online:17 July 2006 InformationCopyright © 1987 Society for Industrial and Applied MathematicsKeywordscontraharmonic meanparallel sumpositive operatorpositive semi-definite matrixvariational formulationMSC codes15A4549A2947D9926D20PDF Download Article & Publication DataArticle DOI:10.1137/0608055Article page range:pp. 670-673ISSN (print):0196-5212ISSN (online):2168-345XPublisher:Society for Industrial and Applied Mathematics