An Enhanced Shifted QR Algorithm for Efficient Eigenvalue Computation of Square Non-Hermitian Matrices

2025/10/15 by Chahat Ahuja, Ahuja, Chahat, Chowdhury, Partha +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2510.13409

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

This work presents a novel approach to compute the eigenvalues of non-Hermitian matrices using an enhanced shifted QR algorithm. The existing QR algorithms fail to converge early in the case of non-hermitian matrices, and our approach shows significant improvement in convergence rate while maintaining accuracy for all test cases. In this work, though our prior focus will be to address the results for a class mid- large sized non-Hermitian matrices, our algorithm has also produced significant improvements in the case of comparatively larger matrices such as 50 x 50 non-Hermitian matrices

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