Near-linear-update algorithm for complex discrepancy

Develop an algorithm for complex discrepancy whose number of updates is linear in n, as suggested by the smoothness properties of the Guillen–Kobzar potential.

Background

The paper explains that its real spectral potential is constrained by the need to maintain a suitable eigenvalue gap and control active-coordinate averages. It contrasts this with the smoothmax potential used by Guillen and Kobzar for complex, equivalently rank-two, discrepancy.

The authors explicitly leave unresolved whether the smoother complex-discrepancy framework can support an algorithm with a linear number of updates. The source text states the target update bound as “$(n)$ updates,” which is reproduced in the quotation; the surrounding discussion identifies the problem as an algorithmic extension of the Guillen–Kobzar approach.