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.

中文翻译：

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新的基于标准的 ℋ-张量，用于识别多元齐次形式的正定性

正定多项式在优化领域很重要。ℋ-张量在识别偶数阶齐次多元形式的正定性方面起着重要作用。在本文中，我们提出了一种识别ℋ-张量的迭代方案，并证明该算法可以在有限的迭代步骤内终止。提供了一些数值例子来说明方法的效率和有效性。