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.↗
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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.↗
Partial derivatives for various scaler functions of matrices
Theorems and their proof are given for the solution of partial derivatives for various scaler functions of matrices.
Quirein, J.↗
An interactive graphics package for the automatic node renumbering of finite element matrices
An interactive graphics software package which allows users to display the non-zero structure of large sparse symmetric materials was described and methods used to implement it as a portable FORTRAN callable subroutine were summarized. In particular, the system permits the display of the resulting matrix after reordering the rows and columns, with the reordering scheme either defined by the user or automatically generated by the program with the aim of reducing matrix bandwidth and profile. Although the primary application of the package has been to the finite element analysis of structures, it is equally well suited to the many other areas of engineering and science which use sparse matrices.
Boisvert, R. F.↗
Recursive partitioned inversion of large (1500 x 1500) symmetric matrices
A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.
Putney, B. H.↗
Euler angles, quaternions, and transformation matrices for space shuttle analysis
Relationships between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion are analyzed, and equations developed are applied directly to current space shuttle problems. The twelve three-axis Euler transformation matrices as functions of the Euler angles, the equations for the quaternion as a function of the Euler angles, and the Euler angles as a function of the transformation matrix elements are included along with a group of utility subroutines to accomplish the Euler matrix, quaternion matrix, and Euler quaternion relationships.
Henderson, D. M.↗
Shuttle Program. Euler angles, quaternions, and transformation matrices working relationships
A brief mathematical development of the relationship between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion is presented. The analysis and equations presented apply directly to current space shuttle problems. The twelve three-axis Euler transformation matrices are given as functions of the Euler angles, the equations for the quaternion as a funtion of the Euler angles, and the Euler angles as a function of the transformation matrix elements.
Henderson, D. M.↗
Chemiluminescent reactions of sulfur /3P2/ atoms in cryogenic matrices - S + O2 yields SO2 /a3 B1/
Results are reported for thermoluminescence studies of reactions of sulfur atoms in cryogenically deposited solid argon through in situ photolysis of OCS. Analysis of the thermoluminescence spectrum that resulted from photolysis and heating of matrices in which O2 was codeposited with an OCS/Ar mixture shows that the emitter contained oxygen derived from the added O2 and that little SO2 accumulated during photolysis. The observed absence of thermoluminescence or fluorescence in either of the allowed transitions of excited SO2 is taken as definitive evidence that ground-state sulfur atoms can insert into the oxygen molecule with effectively zero activation energy.
Long, S. R.↗
Advanced resin matrices for composites
The selection criteria, and the chemical structure of resin matrices are given along with the processing conditions for resins and laminates.
Kourtides, D. A.↗
Analysis of numerical stability and amplification matrices: Fourth-order Runge-Kutta methods
Amplification matrices, numerical kernels, stable, and exponentially stable numerical solutions are examined. The various techniques involved in these concepts are applied to certain systems that have Jordan forms, which are nondiagonal, with particular interest in the case of imaginary or zero eigenvalues.
Kennedy, E. W.↗
Integrating matrices for arbitrarily spaced grid points
Integrating matrices are derived for arbitrarily spaced grid points using either interpolating or least squares fit orthogonal polynomials. Several features of the equally spaced grid case are also discussed.
Lakin, W. D.↗
The matrices of unequilibrated ordinary chondrites - Implications for the origin and history of chondrites
The matrices of 16 unequilibrated chondrites were examined by optical microscopy, an electron microprobe, and a scanning electron microscope. The fine-grained, opaque, silicate matrix of type 3 unequilibrated chondrites was compositionally, mineralogically, and texturally different from the chondrules and their fragments; it may be the low temperature condensate proposed by Larimer and Anders (1967, 1970). Each meteorite has been metamorphosed by a combination of processes including thermal metamorphism and the passage of shock waves; the appearance of each chondrite results from the temperature and pressure conditions which formed it, and subsequent metamorphic alterations.
Huss, G. R.↗
Absorption and resonance Raman spectra of Pb2, Pb3, and Pb4 in xenon matrices
Matrix isolation techniques are used to investigate the spectra of lead molecules and, in particular, to obtain resonance Raman spectra of lead vapors isolated in solid xenon matrices. The presence of Pb2 is confirmed by the visible adsorption, and Raman spectra yield a vibrational frequency for the ground state of 108 per cm and a dissociation energy of 8200 per cm. A second resonance Raman progression indicates a Pb3 species of D3h symmetry. Finally, two additional Raman features at approximately 111 per cm spacing are evidence for a third species, tentatively identified as Pb4.
Stranz, D. D.↗
Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system
Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.
Tsang, W. L.↗