On continuity of Guo Wuwen function
Z. Ambro\.zy, I. Biborski
TL;DR
This paper proves that the functions introduced by Guo Wuwen are continuous and semialgebraic, and uses this to show that the set of realizable nonnegative matrices is closed.
Contribution
It establishes the continuity and semialgebraic nature of Guo Wuwen's functions and demonstrates the closedness of the set of realizable nonnegative matrices.
Findings
Guo Wuwen functions are continuous and semialgebraic
The set of realizable nonnegative matrices is closed
Provides a new understanding of the structure of nonnegative matrices
Abstract
We show that the functions g and gs introduced by Guo Wuwen in [4] are continuous and semialgebraic. We use this fact to prove that the set Nn of ordered n-tuples of real numbers, realizable by nonnegative matrices, is a closed set.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Iterative Methods for Nonlinear Equations · Polynomial and algebraic computation