Results 11 to 20 of about 1,994 (184)
Fast implementation for semidefinite programs with positive matrix completion [PDF]
Optimization Methods and Software, 2015 Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by factorizing the variable matrices. In this paper, we propose a new factorization based on the inverse of the variable matrix
Makoto Yamashita, Kazuhide Nakata
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The complete positivity of symmetric tridiagonal and pentadiagonal matrices
Special Matrices, 2022 We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix AA is completely positive. Our decomposition can be applied to a wide range of matrices.
Cao Lei, McLaren Darian, Plosker Sarah
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The Complexity of Positive Semidefinite Matrix Factorization [PDF]
SIAM Journal on Optimization, 2017 11 ...
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Analysis of Fixing Nodes Used in Generalized Inverse Computation
Advances in Electrical and Electronic Engineering, 2014 In various fields of numerical mathematics, there arises the need to compute a generalized inverse of a symmetric positive semidefinite matrix, for example in the solution of contact problems.
Pavla Hruskova
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On (conditional) positive semidefiniteness in a matrix-valued context [PDF]
Studia Mathematica, 2017 43 pages, replaced Example 4.19 (i) (the original version contained a mistake); journal reference ...
Gesztesy, Fritz, Pang, Michael
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Sufficient conditions to be exceptional
Special Matrices, 2016 A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A
Johnson Charles R., Reams Robert B.
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Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse
Special Matrices, 2020 A real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both ...
Das Joyentanuj +2 more
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A counterexample to the Drury permanent conjecture
Special Matrices, 2017 We offer a counterexample to a conjecture concerning the permanent of positive semidefinite matrices. The counterexample is a 4 × 4 complex correlation matrix.
Hutchinson George
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Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A
Abstract and Applied Analysis, 2013 We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X).
Dongjie Gao
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A trace bound for integer-diagonal positive semidefinite matrices
Special Matrices, 2020 We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.
Mitchell Lon
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