Dimensional analysis, using computer symbolic mathematics

Stoutemyer, David R.

doi:10.1016/0021-9991(77)90054-7

Cited by 9 publications

(6 citation statements)

References 2 publications

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“…The maximum absolute error at the tabulated points was about 4 × 10 −11 , which is two more significant digits than (11) for the same total degree and only one more term. Very gratifying.…”

mentioning

confidence: 81%

“…1. Dimensional analysis can sometimes reduce the number of independent variables, and [11] describes a Maxima program that does this.…”

Section: How To Reduce the Curse Of Dimensionalitymentioning

confidence: 99%

“…(d) Converting the result to recursive form by collecting similar powers of x or asin(x) can significantly reduce the Complexity. For example, rounding coefficients the coefficients in result (11) for brevity, W = 0.78 x + 0.015 x 3 − 0.03 x 2 asin(x)+ (0.076 x + 0.00091 x 3 ) asin(x) 2 + 0.082 asin(x) 3 .…”

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confidence: 99%

“…This is another place where more computer algebra could help Eureqa. (e) Notice that result (11) has no term that is simply a numeric multiple of asin(x).…”

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confidence: 99%

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Can the Eureqa Symbolic Regression Program, Computer Algebra, and Numerical Analysis Help Each Other?

Stoutemyer¹

2013

Notices Amer. Math. Soc.

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The free Eureqa program has recently received extensive press praise. A representative quote is "There are very clever 'thinking machines' in existence today, such as Watson, the IBM computer that conquered Jeopardy! last year. But next to Eureqa, Watson is merely a glorified search engine."The program is designed to work with noisy experimental data, searching for then returning a set of result expressions that attempt to optimally trade off conciseness with accuracy.However, if the data is generated from a formula for which there exists more concise equivalent formulas, sometimes some of the candidate Eureqa expressions are one or more of those more concise equivalents expressions. If not, perhaps one or more of the returned Eureqa expressions might be a sufficiently accurate approximation that is more concise than the given formula. Moreover, when there is no known closed form expression, the data points can be generated by numerical methods, enabling Eureqa to find expressions that concisely fit those data points with sufficient accuracy. In contrast to typical regression software, the user does not have to explicitly or implicitly provide a specific expression or class of expressions containing unknown constants for the software to determine.Is Eureqa useful enough in these regards to provide an additional tool for experimental mathematics, computer algebra users and numerical analysts? Yes, if used carefully. Can computer algebra and numerical methods help Eureqa? Definitely.

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mentioning

confidence: 81%

“…1. Dimensional analysis can sometimes reduce the number of independent variables, and [11] describes a Maxima program that does this.…”

Section: How To Reduce the Curse Of Dimensionalitymentioning

confidence: 99%

mentioning

confidence: 99%

“…This is another place where more computer algebra could help Eureqa. (e) Notice that result (11) has no term that is simply a numeric multiple of asin(x).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Can the Eureqa Symbolic Regression Program, Computer Algebra, and Numerical Analysis Help Each Other?

Stoutemyer¹

2013

Notices Amer. Math. Soc.

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“…This paper presents an efficient and simple numerical method for dimensional arithmetic. The problem of dimensional manipulation can be viewed as one of symbolic mathematics [25,26,17], since dimensions (quantities, units of measurement, see §2) are non-numeric symbols. However, we transform it to a simple numerical problem, and develop an algorithm for this transformed problem.…”

Section: Introductionmentioning

confidence: 99%

Dimensional Analysis in Mathematical Modeling Systems: A Simple Numerical Method

Bhargava¹

1991

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This paper discusses dimensional manipulation, essentially a problem requiring symbolic mathematics techniques, using a numerical approach. The numerical method obeys the laws of dimensional arithmetic. This is achieved by specifying an encoding of units of measurement as prime numbers, and manipulating the resulting expressions numerically. The unique factorization theorem is applied to show that this method makes trivial the problems of dimensional simplification and verification of dimensional equivalency, which are central issues in dimensional arithmetic. The solution has immediate application in mathematical modeling systems, chiefly in the model validation and model solution phases. 'See [17] for a computer solution of the theorem.

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Symbolic-numeric interface: A review

1979

Symbolic and Algebraic Computation

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Dimensional analysis, using computer symbolic mathematics

Cited by 9 publications

References 2 publications

Can the Eureqa Symbolic Regression Program, Computer Algebra, and Numerical Analysis Help Each Other?

Can the Eureqa Symbolic Regression Program, Computer Algebra, and Numerical Analysis Help Each Other?

Dimensional Analysis in Mathematical Modeling Systems: A Simple Numerical Method

Symbolic-numeric interface: A review

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