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Showing 1 to 20 of 85 for “"positive definite"”.
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STRICT REGULARITY OF POSITIVE DEFINITE TERNARY QUADRATIC FORMS
… is to extend the systematic investigation of the positive definite ternary primitive integral quadratic forms and lattices that are candidates for strict regularity. An integer that is primitively represented by a genus, but not by some specific form in that genus, is called a primitive exception …
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Positive definite distributions on semi-simple Lie groups,
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973.
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Some Almost Everywhere Convergence Theorems for Positive Definite Operators
Made available in DSpace on 2014-12-09T22:17:18Z (GMT). No. of bitstreams: 1 6503166.pdf: 1468533 bytes, checksum: bdbac8c178369e41c46e7bd4eeb1ae29 (MD5) Previous issue date: 1964
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Robust stabilization of linear time-invariant uncertain systems via Lyapunov theory
… a Lyapunov function with an uncertain symmetric positive definite matrix P. The uncertain matrix P satisfies the Lyapunov equation A<sup>T</sup>P + PA + Q = 0, where the matrix A is in companion form and the matrix Q is symmetric and positive definite. In the solution of the Lyapunov equation, m …
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Polynomial Preconditioning for Conjugate Gradient Methods
… method is required. When A is hermitian positive definite (hpd), the conjugate gradient method of Hestenes and Stiefel is popular. When A is hermitian indefinite (hid), the conjugate residual method may be used. If A is ill-conditioned, these methods may converge slowly, in which case a …
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Ultraconnected and Critical Graphs
… critical and ultraconnected graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is preserved by Cartesian products. We completely characterize when adding a vertex to an …
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On certain results of Fourier analysis on non-abelian discrete groups.
… will discuss about the characterization of positive definite, radial functions on some non-commutative groups. The subject of positive definite functions is widely studied due to its link with the area of Fourier Multipliers. So, a characterization of positive, definite functions will help …
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Some new results for solving linear systems arising from computational fluid dynamics problems
… problems, Stokes problems, symmetric systems (positive definite or indefinite), and unsymmetric systems. These systems are related, and all of them arise from the numerical solution of partial differential equations. For saddle-point problems, we introduce a class of expansion methods based on …
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Stress analysis of rocket motors with viscoelastic propellant by a mixed finite element model
… The stiffness matrix is transformed from semi-positive definite to positive definite. A rocket motor is composed of (1) case (2) propellant and (3) hollow air core and is modelled as an axisymmetric solid. The propellant of a rocket motor is treated as a viscoelastic material. Static and …
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Structured linear algebra problems and applications to system identification
… for the factorization of the broad class of positive definite Toeplitz-like matrices is given. For nearly semidefinite Toeplitz matrices, it is proven that the Cholesky factor has a limited rank-revealing property. This property has a close connection with a stability result for the Schur …
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The Impact of Sample Size, Prevalence, Estimation Method and Other Factors When Estimating Multilevel Logistic Models
… coverage and width, and likelihood of non-positive definite G-matrices, other key features of multilevel models including the level of random intercept and slope variance and estimation method also impact results. Greater levels of intercept and slope variance tended to decrease mean …
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Solution of Nonsymmetric Systems of Equations on a Multiprocessor
… imaginary axis, or whose symmetric part is not positive definite. This system of equations is solved using the projection methods with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors.
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On the Use of Quasi-Newton Methods for the Minimization of Convex Quadratic Splines
… differentiability conditions. In this work, the positive definite secant update method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) is investigated as a tool to solve the unconstrained minimization problem. It is shown that there is a linear convergence rate and, for nondegenerate problems, …
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A strictly feasible sequential convex programming method
… as possible, i.e., anisotropic, leading to positive definite elasticity tensors, which may be arbitrarily small in case of vanishing material. To guarantee a positive definite global stiffness matrix for computing design constraints, it is required that all iterates of an optimization …
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Riemannian statistical techniques with applications in fMRI
… Functional connectivity matrices are symmetric positive definite (SPD) matrices, but common analysis methods either reduce the functional connectivity matrices to summary statistics or fail to account for the positive definite criteria. However, through the lens of Riemannian geometry functional …
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Iterative Techniques for Radial Basis Function Interpolation
… is equivalent to solving a certain symmetric and positive definite system of equations by Gauss-Seidel iterations. Thus iterative techniques like Jacobi iterations and conjugate gradient methods follow. This symmetric and positive definite system of equations can be derived from the original …
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Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization
… a linear symmetric system Ax=b. When A is not positive definite, the computed search direction may not be a descent direction. Modified Newton methods add a perturbation E to A, so that A+E is positive definite, where E is symmetric positive semidefinite. We study the modified Newton methods in …
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Topics in Optimization and Sparse Linear Systems
… preconditioner for large sparse Symmetric Positive Definite Diagonally Dominant (SPDDD) linear systems. These kinds of linear systems arise in the solution of scalar second order PDEs for Heat Transfer, Electrostatics, Electromagnetics, Ground Water Flow, and Diffusion (with or without …
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