Resona

Mon, 06 Jul 2026 00:00:00 +0300

Resona is a Python library for comprehensive spectral analysis of operators without ever constructing or storing the full matrix — “the FFT of operators.”

Everything runs on a single primitive: the matrix–vector product v ↦ A·v. From that alone, Resona extracts eigenvalues, densities of states, effective rank, pseudospectra and condition numbers; composes operators algebraically via free probability (Pastur subordination, Brown measure for non-Hermitian operators); and even synthesizes new operators matching target spectral properties.

LastSolve

Mon, 06 Jul 2026 00:00:00 +0300

LastSolve wraps any expensive black-box solver — PDE simulators, legacy code, subprocess binaries — learns its behavior from roughly ten strategic calls, and serves the remaining queries in microseconds with validated error bounds. Hence the name: the last few solves you’ll ever pay for.

A single @accelerate decorator gives you transparent surrogate caching. Under it: split-conformal error certification with finite-sample guarantees, parameter identification with Cramér–Rao bounds, bifurcation detection, and blind subspace auditing. The Φ₁ “dial” — Resona’s effective-rank measurement — flags when a cheap surrogate simply doesn’t exist, so the tool knows when not to trust itself.

Projects on Dmitry Serikov

Resona

LastSolve