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7 results

1. NUMERICAL SOLUTION OF THE PROBLEM OF OPTIMUM DISTRIBUTION OF EFFORT.

Author

Miehle, William

Subjects
NUMERICAL analysis, MATHEMATICAL analysis, COMPUTERS, TASKS, MATHEMATICAL optimization, OPERATIONS research, EQUATIONS, ADDITIVE functions, MATHEMATICS
Abstract

This paper is an extension of previously published work by Bernard O. Koopman to the general case of any number of tasks and any effect function. A systematic method for the numerical calculation of the maximum effect and its corresponding optimum distribution is presented in a form which is also suitable for solution on an automatic digital computer. For the special case of additive returns which saturate, a special graphical or numerical method for any number of tasks is presented with an example worked out in detail A similar method for multiplicative effects is sketched. [ABSTRACT FROM AUTHOR]

Published
1954
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2. Applications of Differential Equations in General Problem Solving.

Author

Klopfenstein, R. W.

Subjects
DIFFERENTIAL equations, NUMERICAL analysis, CALCULUS, BESSEL functions, MATHEMATICAL analysis, MATHEMATICS
Abstract

A large class of problems leading to digital computer processing can be formulated in terms of the numerical solution of systems of ordinary differential equations. Powerful methods are in existence for the solution of such systems. A good general purpose routine for the solution of such systems furnishes a powerful tool for processing many problems. This is true from the point of view of ease of programming, ease of debugging, and minimization of computer time. A number of examples are discussed in detail. [ABSTRACT FROM AUTHOR]

Published
1965
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3. Finding Zeros of a Polynomial By the Q-D Algorithm.

Author

Henrici, P., Watkins, Bruce O., and Downing, Jr., A. C.

Subjects
NUMERICAL analysis, POLYNOMIALS, ALGEBRA, MATHEMATICAL analysis, MATHEMATICS, STOCHASTIC convergence
Abstract

A method which finds simultaneously all the zeros of a polynomial, developed by H. Rutishauser, has been tested on a number of polynomials with real coefficients. This slowly converging method (the Quotient-Difference (Q-D) algorithm) provides starting values for a Newton or a Bairstow algorithm for more rapid convergence. Necessary and sufficient conditions for the existence of the Q-D scheme ore not completely known; however, failure may occur when zeros have equal, or nearly equal magnitudes. Success was achieved, in most of the cases tried, with the failures usually traceable to the equal magnitude difficulty. In some cases, computer roundoff may result in errors which spoil the scheme. Even if the Q-D algorithm does not give all the zeros, it will usually find a majority of them. [ABSTRACT FROM AUTHOR]

Published
1965
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4. ON AN EXTREME RANK SUM TEST WITH EARLY DECISION.

Author

Chun, D.

Subjects
MATHEMATICAL analysis, HYPOTHESIS, STATISTICS, NUMERICAL analysis, MATHEMATICAL sequences, MATHEMATICS
Abstract

Where Youden's extreme rank sum test is used, an early decision is often possible by performing the trials in sequence with the following method. After each trial is completed, the greatest lower bound and least upper bound of both extreme rank sums are calculated for all remaining trials. If the critical regions cover either or both intervals of the statistics or the intervals lie completely outside the critical regions, the round-robin test is terminated with the acceptance of the proper hypothesis. [ABSTRACT FROM AUTHOR]

Published
1965
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5. Truncated Version of a Play-the-Winner Rule for Choosing the Better of Two Binomial Populations.

Author

Kiefer, James E. and Weiss, George H.

Subjects
NUMERICAL analysis, PROBABILITY theory, BINOMIAL distribution, BINOMIAL theorem, MATHEMATICS, MATHEMATICAL analysis
Abstract

Results are developed for play-the-winner sampling for choosing the better of two binomial populations when the maximum number of tests is specified. It is shown that for a fixed number of tests the probability of correct selection with alternating assignment exceeds that for play- the-winner sampling. However, when the probability of correct selection is fixed, neither sampling method is uniformly better than the other as measured by the expected number of tests on the poorer population, or on the total expected number of tests. [ABSTRACT FROM AUTHOR]

Published
1974
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6. Finite element solution of nonlinear heat conduction problems with special reference to phase change

Author

O. C. Zienkiewicz, G. Comini, Roland W. Lewis, and S. Del Guidice

Subjects
Numerical Analysis, Mathematical optimization, Applied Mathematics, Mathematical analysis, General Engineering, Relativistic heat conduction, Thermal conduction, Heat capacity, Nonlinear system, Latent heat, Transient (oscillation), Boundary value problem, Heat kernel, Mathematics
Abstract

The paper presents a generally applicable approach to transient heat conduction problems with non-linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration. Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non-linear radiation boundary conditions are given which show very good accuracy. Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.

Published
1974

7. Physical approximation of color-mixture functions

Author

W. E. R. Davies and G. Wyszecki

Subjects
Series (mathematics), business.industry, Numerical analysis, Mathematical analysis, General Engineering, Function (mathematics), Fresnel equations, Photoelectric effect, Set (abstract data type), Optics, Transmittance, Light beam, business, Mathematics
Abstract

One of the most important problems in photoelectric colorimetry is the duplication, by physical means, of a given set of color-mixture functions. Several methods are outlined in this paper for the numerical derivation of close approximations to given color-mixture functions using the relative spectral-sensitivity function of a photoelectric receiver and the spectral transmittances of glass filters. The filters are placed either in series or side by side between the source and the receiver. Numerical examples illustrate the methods.

Published
1962