arXiv subjects

Zhuolin Du

Publications and source records attributed to Zhuolin Du.

3 recordsLinked to original sources

arXiv2026

$\mathrm M$-Eigenpairs of Partially Symmetric Tensors: Exact Reformulation and Perturbation Bounds

In this paper, we consider the computation of $M$-eigenpairs of fourth order partially symmetric tensors arising from elasticity theory. First, a lifted fourth order tensor is constructed, and the original $M$-eigenvalue problem is reformulated as a parameterized generalized tensor eigenvalue problem under the $\mathbf B_{α,β}$-normalization. Then, an exact correspondence between the two eigenvalue problems is established, which provides a procedure for computing all real $M$-eigenpairs through the proposed reformulation. Furthermore, perturbation bounds for the largest $M$-eigenvalue are derived, and the lifted reformulation is shown to preserve these bounds without introducing any additional relaxation. Finally, numerical experiments are reported to show the effectiveness of the proposed method.

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arXiv2026

An Efficient Memory Gradient Method for Extreme M-Eigenvalues of Elastic type Tensors

M-eigenvalues of fourth order hierarchically symmetric tensors play a significant role in nonlinear elastic material analysis and quantum entanglement problems. This paper focuses on computing extreme M-eigenvalues for such tensors. To achieve this, we first reformulate the M-eigenvalue problem as a sequence of unconstrained optimization problems by introducing a shift parameter. Subsequently, we develop a memory gradient method specifically designed to approximate these extreme M-eigenvalues. Under this framework, we establish the global convergence of the proposed method. Finally, comprehensive numerical experiments demonstrate the efficacy and stability of our approach.

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arXiv2025

A Nonparallel Support Tensor Machine for Binary Classification based Large Margin Distribution and Iterative Optimization

Based on the tensor-based large margin distribution and the nonparallel support tensor machine, we establish a novel classifier for binary classification problem in this paper, termed the Large Margin Distribution based NonParallel Support Tensor Machine (LDM-NPSTM). The proposed classifier has the following advantages: First, it utilizes tensor data as training samples, which helps to comprehensively preserve the inherent structural information of high-dimensional data, thereby improving classification accuracy. Second, this classifier not only considers traditional empirical risk and structural risk but also incorporates the marginal distribution information of the samples, further enhancing its classification performance. To solve this classifier, we use alternative projection algorithm. Specifically, building on the formulation where in the proposed LDM-NPSTM, the parameters defining the separating hyperplane form a tensor (tensorplane) constrained to be the sum of rank-one tensors, the corresponding optimization problem is solved iteratively using alternative projection algorithm. In each iteration, the parameters related to the projections along a single tensor mode are estimated by solving a typical Support Vector Machine-type optimization problem. Finally, the efficiency and performance of the proposed model and algorithm are verified through theoretical analysis and some numerical examples.

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