Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T12:44:08.010Z Has data issue: false hasContentIssue false
  • English
  • Français

The SUFFICIENT-POINTS family of propagation operations for intervals on simultaneous linear equations

Published online by Cambridge University Press:  27 February 2009

R. Chen  and
A.C. Ward
R. Chen
Affiliation:
Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, TAIWAN 30043, Republic of China
A.C. Ward
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper defines, develops algorithms for, and illustrates the design use of a class of mathematical operations. These operations accept as inputs a system of linear constraint equations, Ax = b, an interval matrix of values for the coefficients A, and an interval vector of values for either x or b. They return a set of values for the other variable that is “sufficient” in this sense. Suppose that ◯ is an interval of input vectors, and  an interval matrix. Then, one Sufficient-Points operation returns a set of vectors ~ such that for each b in ~, the set of x values that can be produced by inserting all the values of  into Ax = b is a superset of the input vector x. These operations have been partly overlooked by the interval matrix mathematics community, but are mathematically interesting and useful in the design, for example, of circuits.

Keywords

Set-Based DesignFinite ElementsInterval MatricesInternal VectorDesign Compiler
Type
Articles
Information
AI EDAM , Volume 9 , Issue 3 , June 1995 , pp. 211 - 217
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bains, N., & Ward, A. Multiple-type interval propagations through non-monotonic equations. ASME Journal of Mechanical Design (in press).Google Scholar
Chen, R., & Ward, A. (1995a). The RANGE family of propagation operations for intervals on simultaneous linear equations. AI EDAM 9(3), 183–196.Google Scholar
Chen, R., & Ward, A. (1995b). The DOMAIN family of set-propagation operations for systems of linear equations. AI EDAM 9(3), 197–210.Google Scholar
Deif, A. (1986). Sensitivity Analysis in Linear System. Springer-Verlag, New York.CrossRefGoogle Scholar
Finch, W., & Ward, A.Extending generalized interval propagation to monotonic relations among more than three variables. AI EDAM 9(3), 231–242.Google Scholar
Habib, W., & Ward, A. (1991). In pursuit of a design mathematics: Generalizing the labeled interval calculus. 1991 ASME DTM Conference, Miami Beach, pp. 279–284.Google Scholar
Nuding, V., & Wilhelm, J. (1972). Über Gleichungen und über Lösungen. ZAMM 52, T188–90.Google Scholar
Oettli, W., & Prager, W. (1964). Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numer. Math. 6, 405–409.CrossRefGoogle Scholar
Ward, A.C., & Seering, W. (1989). Quantitative inference in a mechanical design compiler. Proceedings of the First International ASME Conference on Design Theory and Methodology, Montreal, Canada, pp. 89–97.Google Scholar