A Non-Triviality Certificate for Scalars and its application to Linear Systems
Abstract
We present an approach of taking a linear weighted Average of N given scalars, such that this Average is zero, if and only if, all N scalars are zero. The weights for the scalars in this Average vary asymptotically with respect to a large positive real. We use this approach with a previous result on Asymptotic Linear Programming, to develop an O(M^4) Algorithm that decides whether or not a system of M Linear Inequalities is feasible, and, whether or not any desired subset of the variables in this system, is permitted to have a non-trivial solution.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2012
- DOI:
- 10.48550/arXiv.1204.1764
- arXiv:
- arXiv:1204.1764
- Bibcode:
- 2012arXiv1204.1764P
- Keywords:
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- Computer Science - Computational Complexity;
- Mathematics - Algebraic Geometry
- E-Print:
- 6 pages, 10 figures, 1 Theorem on the non-triviality Certificate for Scalars