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The symmetric M-matrix and symmetric inverse M-matrix completion problems

Leslie Hogben
2002 Linear Algebra and its Applications  
The techniques used are also applied to matrix completion problems for other classes of symmetric matrices.  ...  The symmetric M-matrix and symmetric M 0 -matrix completion problems are solved and results of Johnson and Smith [Linear Algebra Appl. 290 (1999) 193] are extended to solve the symmetric inverse M-matrix  ...  by B (here sign condition includes nonpositive, nonnegative, sign symmetric or weakly sign symmetric, cf  ... 
doi:10.1016/s0024-3795(02)00301-4 fatcat:s6ahcsubyza6jgcyjkhwjcqhyy

Determining the Dimension and Structure of the Subspace Correlated Across Multiple Data Sets [article]

Tanuj Hasija, Christian Lameiro, Timothy Marrinan, Peter J. Schreier
2019 arXiv   pre-print
We prove that the eigenvalues and eigenvectors of the normalized covariance matrix of the composite data vector, under certain conditions, completely characterize the underlying correlation structure.  ...  Even more challenging is to determine the precise structure of these correlations.  ...  Then all hollow symmetric nonnegative matrices of order at least k and with off-diagonal entries from (ǫ, 1] have at least j nonpositive eigenvalues.  ... 
arXiv:1901.11366v1 fatcat:44xjn3mvnjddhppqyxns4suml4

Algebraic Multigrid for Markov Chains

H. De Sterck, T. A. Manteuffel, S. F. McCormick, K. Miller, J. Ruge, G. Sanders
2010 SIAM Journal on Scientific Computing  
the subdominant eigenvalue satisfies The set of test problems is composed of two classes, those for which the probability transition matrix is similar to a symmetric matrix and for which the eigenvalue  ...  We begin with the problem formulation and definitions in Section 2 and, in Section 3, we provide some essential theoretical background concerning the class of (irreducible) singular M-matrices.  ...  In our experience, problem matrices that are similar to symmetric matrices (and thus have real eigenvalue spectra) often do not require lumping, except sometimes in the first few cycles.  ... 
doi:10.1137/090753589 fatcat:3rephbg42ret7ltzgy2qgvfeze

Column Subset Selection, Matrix Factorization, and Eigenvalue Optimization [chapter]

Joel A. Tropp
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
The primary novelty in this work is an algorithm, based on eigenvalue minimization, for constructing the Grothendieck factorization.  ...  range of the matrix.  ...  The author thanks Ben Recht for valuable discussions about eigenvalue minimization.  ... 
doi:10.1137/1.9781611973068.106 fatcat:2575gcq7nzfehpwmyxmq6qtrvy

Column Subset Selection, Matrix Factorization, and Eigenvalue Optimization

Joel A. Tropp
2008 arXiv   pre-print
The primary novelty in this work is an algorithm, based on eigenvalue minimization, for constructing the Grothendieck factorization.  ...  range of the matrix.  ...  Acknowledgments The author thanks Ben Recht for helpful discussions about eigenvalue minimization.  ... 
arXiv:0806.4404v1 fatcat:agpkz6g5qfblvcdchwbrb2jiei

A Second-Order Cone Based Approach for Solving the Trust-Region Subproblem and Its Variants

Nam Ho-Nguyen, Fatma Kilinç-Karzan
2017 SIAM Journal on Optimization  
We also explore the inclusion of additional hollow constraints to the domain of the TRS, and convexification of the associated epigraph.  ...  Furthermore, under slightly stronger conditions, we give a low-complexity characterization of the convex hull of the epigraph of the nonconvex quadratic function intersected with the constraints defining  ...  We use Matlab notation to denote vectors and matrices. Furthermore, we let I n be the n × n identify matrix and denote the minimum eigenvalue of a symmetric matrix Q as λ Q := λ min (Q).  ... 
doi:10.1137/16m1065197 fatcat:ojmxwxmes5d7dbym2ttzivhs64

Semidefinite Relaxation-Based Optimization of Multiple-Input Wireless Power Transfer Systems

Hans-Dieter Lang, Costas D. Sarris
2017 IEEE transactions on microwave theory and techniques  
Discussions of numerical results yielded by both the closed-form expressions and the refined technique illustrate the importance and practicability of the new method.  ...  It, is shown that this technique offers a rigorous optimization framework for a broad range of current and emerging WPT applications.  ...  M = M T is a symmetric (due to reciprocity of the passive system) hollow matrix containing the mutual impedances jωM n,m .  ... 
doi:10.1109/tmtt.2017.2696948 fatcat:wytaaqnagfdobpc4irpwj5gqly

Flexible Memory Networks

Carina Curto, Anda Degeratu, Vladimir Itskov
2011 Bulletin of Mathematical Biology  
Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices.  ...  Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks.  ...  a submatrix with all nonnegative entries, and "−" a submatrix with all nonpositive entries.  ... 
doi:10.1007/s11538-011-9678-9 pmid:21826564 fatcat:u6yhmudurrbyzkeqz5to3xg2gy

Flexible Memory Networks [article]

Carina Curto, Anda Degeratu, Vladimir Itskov
2011 arXiv   pre-print
Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices.  ...  Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks.  ...  a submatrix with all nonnegative entries, and "−" a submatrix with all nonpositive entries.  ... 
arXiv:1009.4958v2 fatcat:dpkm22k4wferxotjjvtsz5p6g4

Physical interpretation of Newman-Janis rotating systems. II. General systems [article]

Philip Beltracchi, Paolo Gondolo
2021 arXiv   pre-print
In Part I (arxiv:2104.02255), we compared the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and looked for the existence of equations  ...  Here we extend our analysis to general static spherically symmetric systems obtained according to the Drake-Szekeres generalization of the Newman-Janis algorithm.  ...  product of three polynomials and the determinants of matrices with polynomial elements.  ... 
arXiv:2108.02841v2 fatcat:eedhtpqtqnf35i7ssyun4xe6hy

A Stable Penalty Method for the Compressible Navier--Stokes Equations: III. Multidimensional Domain Decomposition Schemes

J. S. Hesthaven
1998 SIAM Journal on Scientific Computing  
The main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible Navier-Stokes equations on conservation form and a unified approach for dealing with the open  ...  The efficacy of the scheme for the compressible Navier-Stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions.  ...  Streett for permitting access to and use of their spectral boundary layer code and to Prof. D. A. Kopriva, Florida State University, for establishing the contact.  ... 
doi:10.1137/s1064827596299470 fatcat:fwlkwnkuwzcnlcoco3htq3urcy

Exactness in SDP relaxations of QCQPs: Theory and applications [article]

Fatma Kılınç-Karzan, Alex L. Wang
2021 arXiv   pre-print
a particular conic subset of the positive semidefinite matrices related to a given QCQP is generated by its rank-one matrices.  ...  Throughout, we will highlight implications of our results for a number of example applications.  ...  Let S n denote the set of real symmetric n × n matrices and S n + the cone of positive semidefinite matrices.  ... 
arXiv:2107.06885v1 fatcat:7issn4cfxngrzjimzff22vy3zm

Rapid evaluation of radial basis functions

George Roussos, Brad J.C. Baxter
2005 Journal of Computational and Applied Mathematics  
For example, the direct evaluation at M locations of a radial basis function interpolant with N centres requires O(MN ) floating-point operations.  ...  This method has been applied to the Hardy multiquadric, the inverse multiquadric and the thin-plate spline to reduce the computational complexity of the interpolant evaluation to O(M + N) floatingpoint  ...  N ) T ∈ R N subject to the conditions N i=1 i p(x i ) = 0, p ∈ m−1 (R d ), the quadratic form N i=1 N j =1 i j (x i − x j ), is nonnegative (or nonpositive) and vanishes only when = 0.  ... 
doi:10.1016/j.cam.2004.10.002 fatcat:2jsfp2gyajdpnmeuk5lgiqbzqi

Edge excitations of paired fractional quantum Hall states

M. Milovanović, N. Read
1996 Physical Review B (Condensed Matter)  
For this system we exhibit a chiral Lagrangian that has manifest SU(2) symmetry but breaks Lorentz invariance because of the breakdown of the spin statistics connection implied by the scalar nature of  ...  The Hilbert spaces of the edge excitations of several "paired" fractional quantum Hall states, namely the Pfaffian, Haldane-Rezayi and 331 states, are constructed and the states at each angular momentum  ...  group of 2ϫ2 integer matrices of determinant 1. ͓  ... 
doi:10.1103/physrevb.53.13559 pmid:9983103 fatcat:3r2wazufgfcevftwculaannwme

Eigenmode Analysis [chapter]

2005 Numerical and Analytical Methods for Scientists and Engineers, Using Mathematica  
100,000-by-100,000 matrices, for example.  ...  The matrices themselves are easy to create using a Note the use of approximate numerical mathematics, rather than exact mathematics, in creating the matrices.  ...  Show that ® s0 if s 0, and for g fixed and k find the angle that provides the maximum value of ® . p g ( ) b A disturbance that is initially spherically symmetric propagates in the qz Ž . 3 Ž . 3 Ž  ... 
doi:10.1002/0471723657.ch4 fatcat:po33lsm5vve4hhf37bdaopvbxi
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