计算张量外反的 $M$-QR 分解和超幂迭代法

Ratikanta Behera, Krushnachandra Panigrahy, Jajati Keshari Sahoo, Yimin Wei
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引用次数: 0

摘要

张量的外逆在计算数学、数值分析和其他张量的广义求逆中发挥着越来越重要的作用。在本文中,我们通过张量 QR 分解和超幂迭代法计算给定张量的具有规定范围和内核的外逆。M-product 结构是张量-张量乘积的一个族,是 t-product 和 c-product 的广义化,允许我们在这些不同模式之间进行物理解释。我们对所提出的基于张量的迭代法的十九阶收敛性进行了理论分析。此外,我们还设计了基于张量的有效算法,利用 M-QR 分解和超幂迭代法计算外倒数。我们用数值实例验证了理论结果,证明了所提方法的适用性。
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$M$-QR decomposition and hyperpower iterative methods for computing outer inverses of tensors
The outer inverse of tensors plays increasingly significant roles in computational mathematics, numerical analysis, and other generalized inverses of tensors. In this paper, we compute outer inverses with prescribed ranges and kernels of a given tensor through tensor QR decomposition and hyperpower iterative method under the M-product structure, which is a family of tensor-tensor products, generalization of the t-product and c-product, allows us to suit the physical interpretations across those different modes. We discuss a theoretical analysis of the nineteen-order convergence of the proposed tensor-based iterative method. Further, we design effective tensor-based algorithms for computing outer inverses using M-QR decomposition and hyperpower iterative method. The theoretical results are validated with numerical examples demonstrating the appropriateness of the proposed methods.
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