Interval-constrained matrix balancing

Yair Censor; Stavros A. Zenios

doi:10.1016/0024-3795(91)90182-V

Interval-constrained matrix balancing

Yair Censor, Stavros A. Zenios

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We define two interval-constrained matrix balancing problems. The models encompass several known formulations of problems that appear in regional input-output analysis, estimation of traffic over transportation and telecommunications networks, and estimation of social accounting matrices. We develop primal-dual, row-action algorithms for the solution of these models and establish their convergence. Both algorithms generalize existing scaling algorithms for equality-constrained matrix balancing problems. One of the algorithms is a generalization of the well-known procedure for matrix balancing called RAS that can handle the range constraints (and is thus called Range-RAS). The structure of the problem makes the algorithm suitable for implementation on massively parallel computers. Details of our implementation on a Connection Machine CM-2 are given. Numerical results for the solution of problems of size up to 500×500 are given, and the performance of the algorithm is compared with that of RAS.

Original language	English
Pages (from-to)	393-421
Number of pages	29
Journal	Linear Algebra and Its Applications
Volume	150
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(91)90182-V
State	Published - May 1991

Bibliographical note

Funding Information:
We appreciate the insightful remarks of an anonymous referee on the first version of this paper. The work of Y. Censor was supported in part by NSF grant ECS-8718971, while visiting the Decision Sciences Department of the Wharton School, University of Pennsylvania, and by NlH grant HG28438 of the Medical image Processing Group (MIPG) of the Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia. The work of S. A. Zenios was supported in part by NSF grant CCR-8811135 and AFOSR grant 89-0145. Access to the Connection Machine CM-2 was made possible through the North-East Parallel Architectures Center (NPAC) at Syracuse University, Syracuse, N.Y., and Thinking Machines Corporation, Cambridge, Mass.

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(91)90182-V

Cite this

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title = "Interval-constrained matrix balancing",

abstract = "We define two interval-constrained matrix balancing problems. The models encompass several known formulations of problems that appear in regional input-output analysis, estimation of traffic over transportation and telecommunications networks, and estimation of social accounting matrices. We develop primal-dual, row-action algorithms for the solution of these models and establish their convergence. Both algorithms generalize existing scaling algorithms for equality-constrained matrix balancing problems. One of the algorithms is a generalization of the well-known procedure for matrix balancing called RAS that can handle the range constraints (and is thus called Range-RAS). The structure of the problem makes the algorithm suitable for implementation on massively parallel computers. Details of our implementation on a Connection Machine CM-2 are given. Numerical results for the solution of problems of size up to 500×500 are given, and the performance of the algorithm is compared with that of RAS.",

author = "Yair Censor and Zenios, {Stavros A.}",

note = "Funding Information: We appreciate the insightful remarks of an anonymous referee on the first version of this paper. The work of Y. Censor was supported in part by NSF grant ECS-8718971, while visiting the Decision Sciences Department of the Wharton School, University of Pennsylvania, and by NlH grant HG28438 of the Medical image Processing Group (MIPG) of the Department of Radiology, Hospital of the University of Pennsylvania, Philadelphia. The work of S. A. Zenios was supported in part by NSF grant CCR-8811135 and AFOSR grant 89-0145. Access to the Connection Machine CM-2 was made possible through the North-East Parallel Architectures Center (NPAC) at Syracuse University, Syracuse, N.Y., and Thinking Machines Corporation, Cambridge, Mass.",

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Interval-constrained matrix balancing

Abstract

Bibliographical note

ASJC Scopus subject areas

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