It is shown how Wengert's procedure for computation of derivatives can be implemented conveniently by use of compiler-generated complex addition, subtraction, and linkage to complex arithmetic subroutines, Evaluat...
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It is shown how Wengert's procedure for computation of derivatives can be implemented conveniently by use of compiler-generated complex addition, subtraction, and linkage to complex arithmetic subroutines, Evaluation of a function and derivative proceed in parallel, as in Wengert's procedure, but with the 'imaginary' parts of variables declared complex bearing the values of the derivatives of the real pads. This technique provides a simple way to compute the derivatives of a function, without the need for deriving and programming the evaluation of explicit formulas for the derivatives. [ABSTRACT FROM AUTHOR]
It is common to need to integrate numerically functions that diverge somewhere outside the range of integration. Even if the divergence occurs quite far away, integration formulas like Simpson's, that depend on fi...
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It is common to need to integrate numerically functions that diverge somewhere outside the range of integration. Even if the divergence occurs quite far away, integration formulas like Simpson's, that depend on fining a polynomial, usually will be inaccurate: near a pole they will be very bad. A method is described that gives formulas that will integrate functions of this kind accurately if the orders and positions of the poles are known. Explicit formulas are given that are easy to use on an automatic computer. It is shown that they can be used for some other singularities as well as poles. If the integral converges, integration can be carried to the singularity. The accuracy of the integration with a pole of second order is discussed, and, as an example, the new formula is compared with Simpson's in the computation of ∫ 0[X] sec[2] π ξ d ξ, 0 < X < 0.5. In this case the new formula is more accurate for X > 0.1, being 30 times as accurate as Simpson's at X = 0.3, 400 times at X = 0.4 and 10[4] times at X = 0.47. Thus, the new formulas are useful even far from the pole, while near the pole their advantage is overwhelming. [ABSTRACT FROM AUTHOR]
A method is presented for the solution of the transportation problem having a cost matrix with few columns. The computer implementation of this method shows it to be very fast and efficient. Applications are indicated...
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A method is presented for the solution of the transportation problem having a cost matrix with few columns. The computer implementation of this method shows it to be very fast and efficient. Applications are indicated for the personnel classification problem as well as the classical transportation problem. An example is worked out in detail. [ABSTRACT FROM AUTHOR]
The article focuses on the use of cascading accumulators in reducing truncation errors associated with numerical integration. When accumulating a large number of quantities as in numerical integration, the sum itself ...
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The article focuses on the use of cascading accumulators in reducing truncation errors associated with numerical integration. When accumulating a large number of quantities as in numerical integration, the sum itself may become much larger than the individual addends. The author here presents a simple and flexible algorithm, which deals also with the case of negative addends. It is important to determine the number of accumulators and the range to be covered by them. These factors are dependent on the characteristics of both the computer and the problem. In most cases an estimate of the final result is known, at least to sufficient accuracy to set an upper limit to the range. The lower limit to the range is given by the size of the smallest addends which occur in sufficient numbers to make a significant contribution to the sum. Most integration routines have a minimum step size, which, when multiplied by the value of the function at its worst behaved point would give a rough estimate, which should be sufficient in most cases.
A method is described for implementing the productions of a context-free phrase structure grammar in a PL/l procedure whose structure and statements parallel the structure and notation of the grammar. [ABSTRACT FROM A...
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A method is described for implementing the productions of a context-free phrase structure grammar in a PL/l procedure whose structure and statements parallel the structure and notation of the grammar. [ABSTRACT FROM AUTHOR]
Examples of algorithms that will accomplish automatic storage reservation without the need for explicit array declarations are described. [ABSTRACT FROM AUTHOR]
Examples of algorithms that will accomplish automatic storage reservation without the need for explicit array declarations are described. [ABSTRACT FROM AUTHOR]
Describes a technique for triple-precision floating-point arithmetic. Machine with a word length of 48 bits; Derivation of the negative of each number with a bit-by-bit complementing of the binary representation; Desc...
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Describes a technique for triple-precision floating-point arithmetic. Machine with a word length of 48 bits; Derivation of the negative of each number with a bit-by-bit complementing of the binary representation; Description of the multiplication and division algorithms.
This article describes a programming technique which makes it possible to program a computer directly from decision tables. A decision table is a tabular form for displaying decision logic. Decision tables have many i...
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This article describes a programming technique which makes it possible to program a computer directly from decision tables. A decision table is a tabular form for displaying decision logic. Decision tables have many inherent advantages. The technique to be illustrated puts these advantages to use in that it enables one to program directly from a decision table. The technique is based on the creation of a binary image of a limited entry decision table in computer memory. Decision tables tend to overcome these objections, and also offer several advantages. Logic is stated precisely and compactly, complex situations are more easily understood, relationships between variables are apparent, and programming is simplified. In addition, the tables provide an excellent form of documentation. The use of decision tables makes it possible to use simplified flowcharts in place of conventional detailed flowcharting. The credit approval table can be used to demonstrate this technique. It should be pointed out that a very simple example was selected in order to facilitate the explanation of the technique. In the large majority of character-oriented computers the bit manipulation as described above can be accomplished.
Various facets of the design and implementation of mathematical expression manipulation algorithms are discussed. Concrete examples are provided by the FORMAC EXPAND and differentiation algorithms, a basic FORMAC util...
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Various facets of the design and implementation of mathematical expression manipulation algorithms are discussed. Concrete examples are provided by the FORMAC EXPAND and differentiation algorithms, a basic FORMAC utility routine, and an experiment in the extraction of the skeletal structure of on expression. One recurrent theme is the need to avoid excessive intermediate expression swell in order to minimize core storage requirements. Although many details from the FORMAC implementation are presented, an attempt is made to stress principles and ideas of general relevance in the design of algorithms for manipulating mathematical expressions. [ABSTRACT FROM AUTHOR]
A new approach to the problem of scheduling course examinations is presented. In principle, an examination schedule which requires a minimum number of examination periods and satisfies the constraint that no student b...
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A new approach to the problem of scheduling course examinations is presented. In principle, an examination schedule which requires a minimum number of examination periods and satisfies the constraint that no student be required to take two examinations simultaneously can be found in two steps. First, courses which may have their examinations scheduled at the same period are grouped together in all possible ways. Then a minimum number of these groups, such that each course is included at least once, are selected. By removing multiple occurrences of courses and then scheduling each group at a different period a minimal schedule can be obtained. Known algorithms for carrying out these procedures are prohibitively expensive. Approximations to the ideal procedure outlined above are given which yield non minimal but feasible schedules with a very small expenditure of time. Results of experiments using these techniques are given. These are encouraging and indicate that further experimentation would be worthwhile. [ABSTRACT FROM AUTHOR]
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