GENERALIZED CHEBYSHEV ACCELERATION

The candidate reproduces the paper’s construction and logic: define pm(λ) = fm(λ/λ1)/fm(1/λ1) from the A2–generalized Chebyshev polynomials fm, use the λ̄-term in the three-term recurrence to introduce a companion matrix M̃, derive the three-term error recursion, and convert it into the explicit iterate update (4.1). Consistency follows from the fixed-point identities Mx+g=x and M̃x+g̃=x together with the normalization that the update coefficients sum to 1. The polynomial-filter form η(m)=pm(M)ε(0) and the Δ-invariance (fm maps Δ to itself) give the norm bound and explain acceleration because |fm(λ/λ1)|≤1 for λ/λ1∈Δ, leaving |fm(1/λ1)| in the denominator to drive down the error, exactly as stated in the paper’s Main Result and discussion of pm(M) (including eqs. (3.4) and (4.1) in the PDF) . The only overreach in the candidate text is the unproved claim of exponential growth of |fm(1/λ1)| for arguments outside Δ; the paper merely asserts that 1/|fm(1/λ1)| “decreases rapidly” and supports it numerically, not with a general theorem . There is also a minor ambiguity in the paper’s description of M̃ (a typographical inconsistency around the diagonalization), which the candidate resolves implicitly by using a “conjugate-eigenvalue” companion operator; this does not affect the core argument .