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arXiv · 2510.18627

Multi-subspace power method for decomposing partially symmetric tensors

Kexin Wang·João M. Pereira·Joe Kileel·Anna Seigal
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Abstract

We present an algorithm for low rank decomposition of tensors of any symmetry type, from fully asymmetric to fully symmetric. It recovers the decomposition one summand at a time via the higher-order power method. This approach is known to fail in general: there need not be a relationship between the summands of a decomposition and the (partially symmetric) singular vector tuples (pSVTs) of the tensor. Our approach overcomes this problem by transforming the input to a tensor with orthonormal slices, via orthogonalization of a flattening. The summands of the decomposition of the original tensor can be recovered from the pSVTs of this new transformed tensor. We introduce a shifted power method for computing pSVTs and prove its global convergence. Numerical experiments demonstrate that our algorithm achieves higher accuracy and faster runtime than existing methods.

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Kexin Wang, João M. Pereira, Joe Kileel, Anna Seigal. 2026-05-20. Multi-subspace power method for decomposing partially symmetric tensors. https://arxiv.org/abs/2510.18627

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