Symbolic mathematical computation---introduction and overview

Tobey, R. G.

doi:10.1145/800204.806261

Cited by 8 publications

(3 citation statements)

References 23 publications

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“…•Cn ~ 7" «-fl/7 Tm x"-\ = (7"_i "+i -7"-i "a; n )/7"_i n _i (14) X\ = (7l »+l ~ 712*2 -7" X 3 • • • )/7ll…”

Section: Hi Analytical Comparison Of Numerical and Symbolic Methodsmentioning

confidence: 99%

“…Neither of these addresses the question of the applicability of symbolic solutions to the dynamic analysis of complex systems. In recent years several modern LISP based symbolic manipulation languages such as REDUCE II [13,14] have become available for most digital computers. The algebraic solution of the equations of motion for many nontrivial problems becomes feasible with these widely available languages.…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

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Application of Symbolic Manipulation to Time Domain Analysis of Nonlinear Dynamic Systems

Dubowsky

Grant

1975

Journal of Dynamic Systems, Measurement, and Control

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The digital computer is often used to perform time domain dynamic analyses of nonlinear systems. Such analyses are notoriously expensive. In many cases this expense is due to algebraic computation with the solution process. Presented is a solution approach, using modem automatic symbolic manipulation techniques, which will result in substantial computational savings for a wide class of problems. Included are guidelines based on fundamental mathematical analysis, to predict which problems will benefit from this simulation approach.

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“…•Cn ~ 7" «-fl/7 Tm x"-\ = (7"_i "+i -7"-i "a; n )/7"_i n _i (14) X\ = (7l »+l ~ 712*2 -7" X 3 • • • )/7ll…”

Section: Hi Analytical Comparison Of Numerical and Symbolic Methodsmentioning

confidence: 99%

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

Application of Symbolic Manipulation to Time Domain Analysis of Nonlinear Dynamic Systems

Dubowsky

Grant

1975

Journal of Dynamic Systems, Measurement, and Control

View full text Add to dashboard Cite

show abstract

“…Thus reasoning about absolute bounds given statistics on antisamples seems a natural application for production systems. It has some similarities to symbolic algebraic manipulation, which often uses this sort of architecture [19]. We can use a number of more sophisticated techniques developed in artificial intelligence to avoid redundant computation in a production system, as for instance relaxation methods or "constraint propagation" [3].…”

mentioning

confidence: 99%