Open Mathematics (Jul 2021)
New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
Abstract
Positive definite polynomials are important in the field of optimization. ℋ-tensors play an important role in identifing the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose an iterative scheme for identifying ℋ-tensor and prove that the algorithm can terminate within finite iterative steps. Some numerical examples are provided to illustrate the efficiency and validity of methods.
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