Results 181 to 190 of about 49,656 (213)

Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems

Journal of Global Optimization, 2003
This paper gives a variety of results on the Euclidean distance matrix completion problem, which is, if some entries of an \(n\times n\) matrix are specified, when can the rest of the matrix be filled in such that it is a matrix of distances between \(n\) points in some Euclidean space, and the related problem of completing a positive semidefinite ...
Huang, Hong-Xuan, Liang, Zhi-An, Pardalos, Panos M.   +2 more
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Actuarial Risk Matrices: The Nearest Positive Semidefinite Matrix Problem

North American Actuarial Journal, 2017
The manner in which a group of insurance risks are interrelated is commonly presented via a correlation matrix. Actuarial risk correlation matrices are often constructed using output from disparate modeling sources and can be subjectively adjusted, for example, increasing the estimated correlation between two risk sources to confer reserving prudence ...
Stefan Cutajar, Helena Smigoc, Adrian O’Hagan   +2 more
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Completing a positive semidefinite matrix as a graph

IOSR Journal of Mathematics
This paper explores the completion of positive semidefinite (PSD) matrices through graph representation, emphasizing the fundamental properties of PSD matrices and their relevance in various applications, including statistics, machine learning, and optimization.
Hawa Ahmed Alrawayati, Ümit Tokeşer
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The unique square root of a positive semidefinite matrix

International Journal of Mathematical Education in Science and Technology, 2006
An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.
Koeber, Martin, Schäfer, Uwe
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The Probability that a (partial) matrix is positive semidefinite

1998
Assuming that a ij is distributed uniformly in [—1,1] and a ii = 1, we compute the probability that a symmetric matrix A = [a ij ] 171-1 j=1 is positive semidefinite. The probability is also computed if A is a Toeplitz matrix. Finally, some results for partial matrices are presented.
C. R. Johnson, G. Nævdal
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Cones of real positive semidefinite matrices associated with matrix stability

Linear and Multilinear Algebra, 1988
Three cones of real positive semidefinite matrices are discussed. Characterizations for Lyapunov diagonal semistability and for Lyapunov diagonal near stability of matrices in terms of these cones are obtained. Also, a relation between Lyapunov diagonal semistability and D-stability is established.
Daniel Hershkowitz, Dafna Shasha
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Cholesky decomposition of a positive semidefinite matrix with known kernel

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dostál, Zdeněk, Kozubek, Tomáš, Markopoulos, Alexandros, Menšík, Martin   +3 more
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Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion

Mathematical Programming, 2010
Optimization problems with nonlinear matrix inequalities, including quadratic and polynomial matrix inequalities, are known as hard problems. They frequently belong to large-scale optimization problems. Exploiting sparsity has been one of the essential tools for solving large-scale optimization problems.
Kim, Sunyoung, Kojima, Masakazu, Mevissen, Martin, Yamashita, Makoto   +3 more
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Joint rank and positive semidefinite constrained optimization for projection matrix

2014 9th IEEE Conference on Industrial Electronics and Applications, 2014
Sparse signals can be sensed with a reduced number of projections and then reconstructed if compressive sensing is employed. Traditionally, the projection matrix is chosen as a random matrix, but a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy.
Qiuwei Li, Shuang Li, Huang Bai, Gang Li, Liping Chang   +4 more
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Shift-invert Lanczos method for the symmetric positive semidefinite Toeplitz matrix exponential

Numerical Linear Algebra with Applications, 2010
Summary: The Lanczos method with shift-invert technique is exploited to approximate the symmetric positive semidefinite Toeplitz matrix exponential. The complexity is lowered by the Gohberg-Semencul formula and the fast Fourier transform. Application to the numerical solution of an integral equation is studied.
Pang, Hong-Kui, Sun, Hai-Wei
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