Abstract
We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak [1] in the case of a quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous term and provide a sufficient condition for its convexity.
Original language | English |
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Article number | 13356 |
Pages (from-to) | 109-123 |
Number of pages | 15 |
Journal | Linear Algebra and Its Applications |
Volume | 488 |
DOIs | |
State | Published - Jan 1 2016 |
Bibliographical note
Publisher Copyright:© 2015 Elsevier Inc.
Keywords
- Convexity
- Joint numerical range
- Quadratic transformation (map)
- Trust region problem
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics