# Circuit Analysis using Monotone+Skew Splitting

arXiv: https://arxiv.org/abs/2211.14010 · HTML: https://mlsanity.com/paper/2211.14010/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Convergence of energy-based learning in linear resistive networks](https://mlsanity.com/paper/2503.00349/) (2025)
- [Circuit realization and hardware linearization of monotone operator equilibrium networks](https://mlsanity.com/paper/2509.13793/) (2025)

## Abstract (arXiv)

It is shown that the behavior of an m-port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a structured skew-symmetric linear operator representing the interconnection structure, together with a linear output transformation. The Condat-V~u algorithm solves inclusion problems of this form, and may be used to solve for the periodic steady-state behavior, given a periodic excitation at each port, using an iteration in the space of periodic trajectories.