1. Numerical ranges of tensors.
- Author
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Ke, Rihuan, Li, Wen, and Ng, Michael K.
- Subjects
- *
NUMERICAL analysis , *CALCULUS of tensors , *GENERALIZATION , *MATRIX norms , *COMPACT spaces (Topology) - Abstract
The main aim of this paper is to generalize matrix numerical ranges to the tensor case based on tensor norms. We show that the basic properties of matrix numerical ranges such as compactness and convexity are valid for tensor numerical ranges. We make use of convexity property to propose an algorithm for approximating tensor numerical ranges in which tensor eigenvalues are contained. Also we consider tensor numerical ranges based on inner products, however, they may not be convex in general. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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