Methods for the direct calculation of reduced density matrices
Methods for direct calculation of reduced density matrices in formulating atomic and molecular quantum mechanics
Simons, J. P.↗
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A perturbation theory in terms of reduced matrices
Perturbation theory for reduced density matrices
Harriman, J. E.↗
Kronecker matrices, computer implementation, and generalized spectra
Closed product form and simplified algorithm for efficient operation of generalized Kronecker matrices, considering role in spectral analysis
Andrews, H. C.↗
Statistical analysis of transition probability matrices in the strong coupled rotational excitation problem
Strong coupled rotational excitation problem in atom-diatomic molecule scattering system, discussing transition probability matrices statistical analysis
Bernstein, R. B.↗
Realization theory of rational transfer matrices
Realization theory of rational transfer matrices presented as fundamental algebraic objects in theory of finite, constant linear systems
Wonham, W. M.↗
Polynomial matrices, representations, and linear system theory
Frequency domain analogies, polynomial matrices, and linear systems
Wolovich, W. A.↗
SAMMSOR 2 - A finite element program to determine Stiffness And Mass Matrices of Shells Of Revolution
Finite element program for determining stiffness and mass matrices of shells of revolution - users manual
Haisler, W. E.↗
Computations with sparse matrices
Sparse matrices inverses and eigenvectors computation methods, giving bibliography
Tewarson, R. P.↗
On the transformation of symmetric sparse matrices to the triple diagonal form
Symmetric sparse matrices transformation to triple diagonal form, giving algorithms for nonzero elements growth minimization
Tewarson, R. P.↗
Perturbation theory in terms of reduced density matrices
Perturbation theory for reduced density matrices representable as functions of independent parameters
Harriman, J. E.↗
Direct calculation of first- and second-order density matrices - The higher RPA method
First and second order density matrices calculation of pure state N fermion systems, using higher random phase approximation
Simons, J.↗
On classes of n-dimensional nonlinear mappings generalizing several types of matrices
Function classes of n-dimensional nonlinear mappings generalizing matrices, including convergence for Jacobi and Gauss-Seidel process
Rheinboldt, W. C.↗
Extreme eigenvalues of Toeplitz matrices associated with certain orthogonal polynomials
Extreme eigenvalues of Toeplitz matrices associated with Laguerre and Jacobi polynomials, using finite difference operators
Baxley, J. V.↗
Program to reduce the size of structural matrices
Computer program was developed to reduce both mass and stiffness matrices by eliminating degrees of freedom using Cholesky decomposition. Program is written in FORTRAN G or H for IBM 360 computer.
Spurlin, H. W.↗
Vlasov equation eigenvalues and eigenvectors for Fourier-Hermite dispersion matrices of order greater than 1,000
The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).
Grant, F. C.↗
Power series evaluation of transition and covariance matrices.
Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.
Bierman, G. J.↗
Criteria for selecting resin matrices for improved composite strength
Criteria are presented which can be used a priori to select matrices to yield composites with improved unidirectional strength. The criteria evolved from an investigation including both theoretical and experimental efforts. Composite micromechanics were used in conjunction with suitable experiments and reference data to identify those matrix properties which influence composite strength properties. Composites of graphite fibers and low, intermediate and high-modulus resins were investigated. It was found that the area under the matrix stress/strain diagram limited to one percent strain is a good index for an a priori assessment of the matrix contribution to composite strength. The corresponding initial modulus is a useful parameter in translating matrix properties to composite properties. Matrix properties such as ultimate strength, ultimate elongation, toughness, and fracture toughness are misleading in translating matrix properties to composite strength.
Chamis, C. C.↗
Criteria for selecting resin matrices for improved composite strength.
Criteria are presented which can be used a priori to select matrices to yield composites with improved unidirectional strength. The criteria evolved from an investigation including both theoretical and experimental efforts. Composite micromechanics were used in conjunction with suitable experiments and reference data to identify those matrix properties which influence composite strength properties. Composites of graphite fibers and low, intermediate and high-modulus resins were investigated. It was found that the area under the matrix stress/strain diagram limited to one percent strain is a good index for an a priori assessment of the matrix contribution to composite strength. The corresponding initial modulus is a useful parameter in translating matrix properties to composite properties.
Chamis, C. C.↗