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Complementary pivot algorithms known at the present time fall into several quite general categories, with obvious similarities. This paper deals with general pivoting systems which provide a natural setting for the study of complementary pivot algorithms. A generalized algorithm is presented for these systems. We give results on the number of iterations necessary for such an algorithm.

In this paper a generalized algorithm for unconstrained optimization based on homogeneous functions is presented. It is shown that this generalized algorithm reaches the minimum of a homogeneous function inn + 2 iterations and does not require finding the minimum on the one-dimensional search. The Jacobson and Oksman algorithm can be derived from this general algorithm.

A generalized algorithm for estimating the proportion of total variance that one multivariate measurement battery explains in another is described. The generality of the algorithm is exemplified empirically by comparing and contrasting solutions based on alternative methods of orthogonalizing the same basic data. The results observed on the computed examples underscore 3 important characteristics of measures of interbattery association.

In this article an algorithm is developed to solve the equations for one-dimensional unsteady flow of compressible fluids in the presence of area change, wall friction, heat transfer, and entropy gradients. The algorithm is based on a rectangular mesh solution of the cor responding characteristics equations in the space-time plane. It is arranged in a generalized form to permit convenient application to a variety of engineering systems. A model of the gas exchange process occurring in a two-stroke internal combustion engine with intake and exhaust ducts is used to demonstrate application of the algorithm and to observe the accuracy and stability of solutions with varying mesh-step size.

The linear least-mean-square error (LMS) estimate of a scalar random variable given an observation of a vector-valued random variable (data) is well know. Computation of the estimate requires knowledge of the data correlation matrix. Algorithms have been proposed by Griffiths [9] and by Widrow [7] for iterative determination of the estimate of each element from a sequence of scalar random variables given an observation of the corresponding element from a sequence of date vectors when the data correlation matrix is not known. These algorithms are easy to implement, require little storage, and are suitable for real-time processing. Past convergence studies of these algorithms have assumed that the data vectors were mutually independent. In this study some asymptotic properties of these and other related algorithms are derived for a sequence of mutually correlated data vectors. A generalized algorithm is defined for analytic purposes. It is demonstrated for this generalized algorithm that excess mean-square error (as defined by Widrow) can be made arbitrarily small for large values of time in the correlated case. The analysis can be applied to a particular estimation scheme of 1) the particular algorithm can be placed in the generalized form, and 2) the given assumptions are satisfied. The analysis of the generalized algorithm requires that the data vectors possess only a few properties; foremost among these are ergodicity and a form of asymptotic independence. This analysis does not assume any particular probability distribution function nor any particular form of mutual correlation for the data vectors.

In this paper, a unified method to construct quadratically convergent algorithms for function minimization is described. With this unified method, a generalized algorithm is derived. It is shown that all the existing conjugate-gradient algorithms and variable-metric algorithms can be obtained as particular cases. In addition, several new practical algorithms can be generated. The application of these algorithms to quadratic functions as well as nonquadratic functions is discussed.

A generalized algorithm for the estimation of parameters in a process model from experimental data is presented in this paper. The algorithm, which combines linear programming with quasilinearization, is formulated and its advantages and limitations are discussed. Examples are included to illustrate application of the algorithm to real engineering problems, one of which was encountered in industry and another of which was encountered in a control study. The examples demonstrate the incorporation of constraints, convergence promotion and reliability estimates into the identification. On presente dans le present travail un algorithme generalise, pour levaluation des parametres, a partir de resultats experimentaux dans un modele de processus. On formule lealgorithme, qui combine la programmation lineaire avec la quasilinearisation et discute ses avantages et ses limitations. Des exemples illustrent leapplication de lealgorithme a des problemes reels de genie, dont leun est industriel et un autre provient deune cation des contraintes, de la promotion de la convergence et des etude de contrǒle; ils demontrent leincorporation dans leidentifiestimes de fiabilite.

In this paper the Mattson-Solomon algorithm is generalized in several directions. Based on the generalized algorithm, several classes of Bose-Chaudhuri-Hocquenghem codes are given and shown to possess minimum distance of values greater than those given by the Bose-Chaudhuri-Hocquenghem bound.

The most generalized algorithm for the least-squares estimation of parameters in nonlinear, implicit models is the modified Deming approach. This technique is very complicated; however, simpler approaches for many problems lead to reasonable solutions. One widely accepted alternative is the Δ transformation of Hust and McCarty. This article offers another equally simple alternative: geometrically transformed weights.