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Structural solvability of systems of equations —A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems—

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Abstract

Structural solvability of systems of equations is discussed on the basis of the observation that two kinds of numbers—one of which is accurate and the other inaccurate but independent—are to be distinguished in the mathematical modelling of physical/engineering systems. The concept of mixed matrix is introduced along with its basic mathematical properties; in particular, the rank of a mixed matrix is expressed as the maximum size of a common independent set of two matroids associated with it.

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Authors and Affiliations

  1. Institute of Socio-Economic Planning, University of Tsukuba, Sakura-mura, 305, Ibaraki, Japan

    Kazuo Murota

  2. Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo, Bunkyo-ku, Hongo, 113, Tokyo, Japan

    Masao Iri

Authors
  1. Kazuo Murota
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  2. Masao Iri
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Additional information

Part of this paper is published in a Japanese journal [25].

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Murota, K., Iri, M. Structural solvability of systems of equations —A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems—. Japan J. Appl. Math. 2, 247–271 (1985). https://doi.org/10.1007/BF03167048

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  • DOI: https://doi.org/10.1007/BF03167048

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