03177nam 22006014a 450 991045429550332120200520144314.01-281-93563-89786611935634981-279-521-9(CKB)1000000000537829(DLC)2004269154(StDuBDS)AH24685168(SSID)ssj0000127202(PQKBManifestationID)11936900(PQKBTitleCode)TC0000127202(PQKBWorkID)10051708(PQKB)10571981(MiAaPQ)EBC1681529(WSP)00005273(PPN)18135621X(Au-PeEL)EBL1681529(CaPaEBR)ebr10255679(CaONFJC)MIL193563(OCoLC)815752525(EXLCZ)99100000000053782920040205d2003 uy 0engur|||||||||||txtccrCompletely positive matrices[electronic resource] /Abraham Berman, Naomi Shaked-Monderer[River Edge] New Jersey World Scienficc20031 online resource (ix, 206 p. ) illBibliographic Level Mode of Issuance: Monograph981-238-368-9 Includes bibliographical references (p. 193-197) and index.ch. 1. Preliminaries. 1.1. Matrix theoretic background. 1.2. Positive semidefinite matrices. 1.3. Nonnegative matrices and M-matrices. 1.4. Schur complements. 1.5. Graphs. 1.6. Convex cones. 1.7. The PSD completion problem -- ch. 2. Complete positivity. 2.1. Definition and basic properties. 2.2. Cones of completely positive matrices. 2.3. Small matrices. 2.4. Complete positivity and the comparison matrix. 2.5. Completely positive graphs. 2.6. Completely positive matrices whose graphs are not completely positive. 2.7. Square factorizations. 2.8. Functions of completely positive matrices. 2.9. The CP completion problem -- ch. 3. CP rank. 3.1. Definition and basic results. 3.2. Completely positive matrices of a given rank. 3.3. Completely positive matrices of a given order. 3.4. When is the cp-rank equal to the rank?A real matrix is positive semidefinite if it can be decomposed as A=BB[symbol]. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB[symbol] is known as the cp-rank of A. This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined.MatricesElectronic books.Matrices.512.9/434Berman Abraham42972Shaked-Monderer Naomi906214MiAaPQMiAaPQMiAaPQBOOK9910454295503321Completely positive matrices2026800UNINA02876nam 2200565 a 450 991073944060332120260331110520.0978129933740412993374069781461463870146146387410.1007/978-1-4614-6387-0(OCoLC)834544693(MiFhGG)GVRL6XJO(CKB)2670000000336417(MiAaPQ)EBC1106323(MiFhGG)9781461463870(MiFhGG)9781461463863(EXLCZ)99267000000033641720130111d2013 uy 0engurun|---uuuuatxtccrStructure of solutions of variational problems /Alexander J. Zaslavski1st ed. 2013.New York Springer20131 online resource (viii, 115 pages)SpringerBriefs in optimization,2190-8354"ISSN: 2190-8354.""ISSN: 2191-575X (electronic)."9781461463863 1461463866 Includes bibliographical references and index.Preface -- 1. Introduction -- 2. Nonautonomous problems -- 3.Autonomous problems -- 4.Convex Autonomous Problems -- References -- Index.Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line.  Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations  are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property  in individual  (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians  working in optimal control and the calculus as  well as with graduate students.SpringerBriefs in optimization.Calculus of variationsCalculus of variations.516.3516.36Zaslavski Alexander J721713MiAaPQMiAaPQMiAaPQBOOK9910739440603321Structure of Solutions of Variational Problems3552709UNINA