positive semidefinite
Positive semidefinite intervals for matrix pencils.
... combine these results to obtain the positive semidefinite interval when A is nonsingular but indefinite. Chapter 5 presents remarks on imple- mentation and includes examples. Concluding[r] ...
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A Generative Word Embedding Model and its Low Rank Positive Semidefinite Solution
... Based on the above considerations, we pro- pose to unify the embeddings of words and con- text words. Our link function factorizes into three parts: the interaction of two embeddings capturing linear correlations of two ...
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Dykstra’s Algorithm for the Optimal Approximate Symmetric Positive Semidefinite Solution of a Class of Matrix Equations
... In this paper, we propose a new algorithm to compute the optimal approximate symmetric positive semidefinite solution of Equation (1.3). We state Problem I as the minimization of a convex quadratic function ...
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Compressing Positive Semidefinite Operators with Sparse/Localized Bases
... a positive semidefinite (PSD) operator, such as a PSD matrix, an ellip- tic operator with rough coefficients, a covariance operator of a random field, or the Hamiltonian of a quantum system, we would like ...
224
Positive Semidefinite Metric Learning Using Boosting-like Algorithms
... remains positive semidefinite. Semidefinite programming is often used to enforce this constraint, but does not scale well and is not easy to ...any positive semidefinite ma- trix can be ...
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Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach
... This example illustrates that the main ingredients to obtain a concrete algorithm are convenient formulas for the gradient and for the retraction mapping. This paper provides such formulas for three examples of nonlinear ...
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Trace inequalities for positive semidefinite matrices with centrosymmetric structure
... Trace inequalities for positive semidefinite matrices with centrosymmetric structure Di Zhao1, Hongyi Li1* and Zhiguo Gong2 * Correspondence: [email protected] 1 LMIB, School of Math[r] ...
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Positive Semidefinite Matrices, Exponential Convexity for Majorization, and Related Cauchy Means
... In this paper, we prove positive semidefiniteness of matrices generated by differences deduced from majorization-type results 1.9, 1.11, 4.2, and 4.5 which implies exponential convexity and log-convexity of these ...
19
Development of Interest in Science and Interest in Teaching Elementary Science: Influence of Informal, School, and Inquiry Methods Course Experiences
... In this thesis, we provide a detailed overview of the basic functions of matrices while focusing on the square root function of a matrix and a few of the most common computational methods. We discuss the specific case of ...
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Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation
... differences between the lower and upper bounds are small, though equalities are replaced by positive semidefinite (PSD) constraints. While in the periodogram-based scheme, the linear constraint helps to ...
19
Learning the Kernel Matrix with Semidefinite Programming
... It is important to observe that we do not necessarily need to choose a kernel function, specifying the inner product between the images of all possible data points when mapped from an input space X to an appropriate ...
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Matrix positivity preservers in fixed dimension
... to positive semidefinite matrices of arbitrary ...of positive semidefinite matrices, and a sharp asymptotic bound for the matrix cube problem involving Hadamard ...
6
Some inequalities for unitarily invariant norms of matrices
... Mathematical Subject Classification: MSC 2010 15A60; 47A30; 47B15 Keywords: Unitarily invariant norms, Positive semidefinite matrices, Convex function, Inequality.. So, UAV = A for all A[r] ...
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Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
... not positive semidefinite or an entanglement witness [13], then there will necessarily be local measurements such that the resulting ~p is not a good probability vector, because some of the entries will be ...
20
A Subspace Iteration for Calculating a Cluster of Exterior Eigenvalues
... The ability of the new method to compute a left-side cluster is illustrated in Table 3. Note that the Type B matrix and the Type C matrix are positive semidefinite matrices, in which the left-side cluster ...
14
Computation of Real Radical Ideals by Semidefinite Programming and Iterative Methods
... In this chapter, we use facial reduction approach to e ff ectively reduce the size of the moment matrix and then solve the reduced problem using the Douglas-Rachford reflection method. Fi- nally we recover the ...
150
On Sampling Complexity of the Semidefinite Affine Rank Feasibility Problem
... a positive semidefinite constraint, so the results of this paper can be extended to rank minimization problems as ...a semidefinite ma- trix with all diagonal entries equal to 1 is N P-hard as soon ...
8
Low Rank Positive Approximants of Symmetric Matrices
... symmetric positive semidefinite matrix which is nearest to X with regard to a certain matrix ...given positive integer such that 1 ≤ ≤ − n 1 , and define ...
15
Maximum Principles for Normal Matrices
... As in the former cases it is easy to verify that when using the trace norm on a positive semidefinite hermitian matrix the last assertion is reduced to Ky Fan maximum principle.. It shou[r] ...
9
Simultaneous kernels of matrix Hadamard powers
... is positive semidefinite, it follows by the PSRP that each subvector of the last row and column of C determined by this partition is a multiple of the vector with entries all 1 of the appropriate size by a ...
12