A practical all-time bound for a three-block Aluthge transition
Year: 2026
Type: preprint
Abstract: We give an evaluated candidate error bound for ordinary Aluthge iteration (weight 1/2) on three Jordan blocks of sizes (1,1,2) joined by entries 1/128. In a specified moving triangular gauge, the Frobenius distance between the scaled discrete orbit and its entrance-normalized bidiagonal reference is at most 21/100 at every integer time m >= 128. The finite part checks all 65,409 integers through 65,536 with ball arithmetic. The infinite part uses explicit ratio envelopes and logarithmic non-expansion: a checked entry condition and uniform local remainder bounds prevent the orbit from leaving a fixed chart and make the accumulated defect summable. The reference entrance error, matrix square-root enclosure and coefficient remainder are included. A small exact-rational checker verifies the final conditional tail inequalities; it does not replace the finite orbit computation or analytic proof. The result concerns this fixed instance, not an input box or a new general transition theorem. The claim remains a provisional candidate.
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: W7225244027