The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a non-symmetric complex tensor and unitary symmetric eigenpairs (US-eigenpairs) of its symmetric embedding tensor is established. An Algorithm 3.1 is given to compute the U-eigenvalues of non-symmetric complex tensors by means of symmetric embedding. Another Algorithm 3.2, is proposed to directly compute the U-eigenvalues of non-symmetric complex tensors, without the aid of symmetric embedding. Finally, a tensor version of the well-known Gauss–Seidel method is developed. Efficiency of these three algorithms are compared by means of various numerical examples. These algorithms are applied to compute the geometric measure of entanglement of quantum multipartite non-symmetric pure states.

中文翻译：

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计算非对称复张量U特征值的迭代方法及其在量子纠缠中的应用

本文的目的是研究计算非对称复张量的unit特征值（U-特征值）的问题。通过复数张量的对称嵌入，建立了非对称复数张量的U-本征对与其对称嵌入张量的unit对称本征对（US-本征对）之间的关系。给出了算法3.1，通过对称嵌入来计算非对称复张量的U-特征值。提出了另一种算法3.2，​​无需借助对称嵌入就可以直接计算非对称复张量的U特征值。最后，开发了著名的高斯-塞德尔方法的张量版本。通过各种数值示例比较了这三种算法的效率。