## 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 |
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Pages (from-to) | 393-421 |

Number of pages | 29 |

Journal | Linear Algebra and Its Applications |

Volume | 150 |

Issue number | C |

DOIs | |

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