The algebra of probability density functions
Algebra of probability density functions of variable known as arbitrary function of one or more random variables
Grunebaum, B. G.↗
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Algebraic methods for control system analysis and design Final report, Apr. 1967 - Apr. 1969
Algebraic methods for analysis and design of control systems
Siljak, D. D.↗
Spectral density sum rules, current algebra, and zero-mass extrapolations.
Partially conserved axial vector currents and current algebra to obtain vertex functions at point having zero mass by extrapolations
Dooher, J.↗
Toward an algebraic theory of the analysis and testing of digital networks.
Logic networks of Boolean analogs analyzed by algebraic signal flow theory, introducing variational derivative for test detection in combinational and sequential networks
Brown, A.↗
Smithsonian package for algebra and symbolic mathematics
Symbolic programming system for computer processing of algebraic expressions
Cherniack, J. R.↗
Algebraic criterion for absolute stability, optimality, and passivity of dynamic systems
Dynamic systems absolute stability, optimality and passivity algebraic criterion in terms of real even polynomial coefficients
Siljak, D.↗
Algebraic criterion for absolute stability, optimality and passivity of dynamic systems
Necessary and sufficient conditions on coefficients of real nonnegative polynomial pi/omega/, obtaining algebraic criterion for stability, optimality and passivity of dynamic linear systems
Siljak, D. D.↗
Algebraic test for passivity
Algebraic criterion for positive realness of rational functions, using Routh algorithm
Siljak, D. D.↗
Automated algebraic manipulation in celestial mechanics
Automated algebraic manipulation in celestial mechanics, discussing use of Poisson series in perturbation theory problem
Jefferys, W. H.↗
Pauli-algebraic operators in polarization optics
Analysis and synthesis of linear optical systems involving polarization effects by Pauli algebra of complex second order matrices
Whitney, C.↗
Algebraic theory of finite Fourier transforms
Finite Fourier transforms from finite dimensional algebraic viewpoint, deriving fast Fourier transform algorithm via tensor products induced matrix factorization
Nicholson, P. J.↗
Algebraic, geometric, and stochastic aspects of genetic operators
Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.
Foo, N. Y.↗
Numerical stability in problems of linear algebra.
Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
Babuska, I.↗
Lie algebras and linear differential equations.
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
Brockett, R. W.↗
Computer programs for the solution of systems of linear algebraic equations
FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.
Sequi, W. T.↗
On the algebraic structure of bilinear systems.
It is shown that a particular bilinear model is both quite general and easy to work with. A basic structure theory is developed with the aid of previous results. Some preliminary ideas are discussed together with the system interconnection, the canonical form, questions of controllability, aspects of observability, and equivalent realizations. It is pointed out that in actually determining equivalent realizations for systems and in the classification of systems, the results available in the study of Lie algebras are of fundamental importance.
Brockett, R. W.↗
Algebraic criteria for positive realness relative to the unit circle.
A purely algebraic algorithm is developed for testing positive real character of real rational functions and matrices relative to the unit circle in the complex plane. Since the algorithm is entirely recursive and is performed in finite number of steps, it is suitable for machine computations.
Siljak, D. D.↗