Algorithmic Conversion of Numerical Tensor Decompositions to Functional APA Schemes

Develop an algorithmic procedure that converts numerical tensor decompositions obtained for arbitrary-precision approximate matrix multiplication into symbolic decompositions with functional entries.

Background

The paper explains that existing searches for APA algorithms often produce approximate floating-point tensor decompositions. To obtain implementable APA schemes, these numerical decompositions must be converted into symbolic decompositions whose entries are functions of the evaluation parameter. The authors state that no algorithmic method for this conversion is known, identifying a methodological gap in the construction of APA algorithms.

References

There is no known algorithmic way to do this.

— Fast and Stable Arbitrary Precision Approximate Matrix Multiplication  (2610.13905 - Dumitriu et al., 9 Oct 2026) in Section 1, Introduction

Since our goal in this section is to demonstrate stability for \cref{alg:alt_basis_APA_exact}, we leave an APA extension of these results to future work.

— Fast and Stable Arbitrary Precision Approximate Matrix Multiplication  (2610.13905 - Dumitriu et al., 9 Oct 2026) in Section 5, Remark following the statement of the stability bounds