Representing super-sparse matrices with perturbed values

Authors:
Harvey J. Greenberg;Richard P. O'Neill
Affiliations:
Office of Analysis Oversight and Access, Washington, DC;Office of Energy Source Analysis, Washington, DC
Venue:
Communications of the ACM
Year:
1981

Citing 3
Cited 0

The art of computer programming, volume 3: (2nd ed.) sorting and searching

The art of computer programming, volume 3: (2nd ed.) sorting and searching
Some Design Features of a Sparse Matrix Code

ACM Transactions on Mathematical Software (TOMS)
Aspects of large-scale in-core linear programming

ACM '71 Proceedings of the 1971 26th annual conference

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Abstract

This paper describes a form of purposeful data perturbation in a linear programming model which pertains to uncertainties in the magnitudes of the matrix coefficients. A problem in value pool construction is described first, then a resolution based on a new concept, “covering lattices.” Computer representations of real values, limited by finite precision, is an example of a covering lattice. After presenting the strategy and tactical variations, the effects of resident distortion are analyzed. Several theorems are presented that measure bias under a variety of assumptions. An appendix is included that contains mathematical proofs.