I will discuss the existence of an open set of n1× n2× n3 tensors of rank r on which a popular algorithm for computing tensor rank decompositions is numerically unstable. The algorithm is based on a reduction to a linear matrix pencil followed by a generalized eigendecomposition (it is sometimes called ``Jenrich’s algorithm”). The instability is caused by the fact that the condition number of the tensor rank decomposition can be much larger for n1×n2×2 tensors than for the original n1×n2×n3 input tensor. Joint work with Carlos Beltran and Nick Vannieuwenhoven.
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