On the Positive Definite Solutions of a Nonlinear Matrix Equation [PDF]
Journal of Applied Mathematics, 2013 The positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.
Panpan Liu, Shugong Zhang, Qingchun Li
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Integer Factorization of a Positive-Definite Matrix [PDF]
SIAM Journal on Discrete Mathematics, 2015 This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension of the matrix.
Tropp, Joel A.
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On matrix valued square integrable positive definite functions [PDF]
Monatshefte für Mathematik, 2015 11 ...
Hongyu He, He, Hongyu
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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation [PDF]
Journal of Applied Mathematics, 2014 The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1 ...
Jing Li, Yuhai Zhang
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Positive definite solution of two kinds of nonlinear matrix equations [PDF]
Surveys in Mathematics and its Applications, 2009 Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X=Σi=1m Ai* XδiAi and X=Σi=1m (Ai* XAi)δi ...
Fujian Duan, Zhenyun Peng, Xuefeng Duan
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The Space of a Positive Definite Matrix of Measures and Density of Matrix Polynomials inL1 [PDF]
Journal of Approximation Theory, 1997 AbstractIn this paper we study the space Lp(μ), 1⩽p⩽+∞,μbeing a positive definite matrix of measures. We prove that the set of all positive definite matrices of measures having the same moments as those ofμis compact in the vague topology, and we give a density result for L1(μ) which is an extension to the matrix case of the classical result for scalar
Duran, Antonio J. +1 more
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Identification of a Positive Definite Mass Matrix
Journal of Vibration and Acoustics, 1988 In system identification it is important that any a priori information about the system is utilized in the processing of measured data. Structural vibration problems can be modelled in terms of mass, stiffness, and damping and it is usually the case that the mass matrix is positive definite.
John E. Mottershead +2 more
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An algorithm for rescaling a matrix positive definite [PDF]
Linear Algebra and its Applications, 1987 Given a square matrix M, find D diagonal, so that DM is positive definite, i.e. has its field of values in the right half plane. Here it is shown that this problem can be formulated as an infinite set of linear inequalities, and solved by solving a finite sequence of linear programming problems.
Hu, Hui
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Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers [PDF]
, 1990 In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method.
Levkovitz, R +3 more
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The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
International Journal of Nonlinear Sciences and Numerical Simulation, 2017 Abstract: In this paper, we study the nonlinear matrix equation X s
Zhang, Xindong, Feng, Xinlong
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