Quantitative bounds for the three-block Aluthge transition
Year: 2026
Type: preprint
Abstract: Three fixed Jordan blocks are joined by two positive links that vanish as powers of a small parameter. A candidate quantitative bound is given for ordinary half Aluthge iteration across the transition between balanced and separated mergers. In a moving triangular gauge, the profile error against the calibrated positive bidiagonal reference is bounded uniformly for all m >= m0 by C[(m0+1)^(-rho)+epsilon^eta], for fixed 0 < rho < 1/2 and a constructible eta > 0. The exponent gap may lie in an arbitrary shrinking envelope, independently of the diverging lower observation time. Cubic tangency, energy decay and polynomial finite-prefix sensitivity permit a power-scale prefix; whole-cut division, exact calibration and a non-expansive logarithmic comparison control the entire future without a waiting-duration factor. Data and block sizes are fixed and links are real positive. Constant constructions have terminating mathematical recipes but general numerical values and a practical accuracy certificate are not implemented. Results remain provisional candidates.
Author: Barritz, Robert
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225019456