Three decompositions of symmetric tensors have similar condition numbers

10/08/2021

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We relate the condition numbers of computing three decompositions of symmetric tensors: the canonical polyadic decomposition, the Waring decomposition, and a Tucker-compressed Waring decomposition. Based on this relation we can speed up the computation of these condition numbers by orders of magnitude

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Three decompositions of symmetric tensors have similar condition numbers

Symmetric Tensor Decompositions On Varieties

The condition number of many tensor decompositions is invariant under Tucker compression

On condition numbers of symmetric and nonsymmetric domain decomposition methods

Unitary canonical forms over Clifford algebras, and an observed unification of some real-matrix decompositions

Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective

Gohberg-Kaashoek Numbers and Forward Stability of the Schur Canonical Form

GR decompositions and their relations to Cholesky-like factorizations

Three decompositions of symmetric tensors have similar condition numbers

Related Research

Symmetric Tensor Decompositions On Varieties

The condition number of many tensor decompositions is invariant under Tucker compression

On condition numbers of symmetric and nonsymmetric domain decomposition methods

Unitary canonical forms over Clifford algebras, and an observed unification of some real-matrix decompositions

Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective

Gohberg-Kaashoek Numbers and Forward Stability of the Schur Canonical Form

GR decompositions and their relations to Cholesky-like factorizations