This paper is concerned with the solution of severely ill-conditioned linear tensor equations. These kinds of equations may arise when discretizing partial differential equations in many space-dimensions by finite difference or spectral methods. The deblurring of color images is another application. We describe the tensor Golub–Kahan bidiagonalization (GKB) algorithm and apply it in conjunction with Tikhonov regularization. The conditioning of the Stein tensor equation is examined. These results suggest how the tensor GKB process can be used to solve general linear tensor equations. Computed examples illustrate the feasibility of the proposed algorithm.

中文翻译：

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病态张量方程的Golub–Kahan双角化及其应用

本文关注的是病态严重的线性张量方程的解。当通过有限差分或频谱方法在许多空间维中离散偏微分方程时，可能会出现这类方程。彩色图像去模糊是另一种应用。我们描述了张量Golub–Kahan的对角化（GKB）算法，并将其与Tikhonov正则化结合使用。检查斯坦因张量方程的条件。这些结果表明，张量GKB过程可用于求解一般线性张量方程。算例说明了该算法的可行性。