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<p>We present an efficient method for computing dominant eigenvalues of large, nonsymmetric, diagonalizable matrices based on an adaptive block Lanczos algorithm combined with Chebyshev polynomial filtering. The proposed approach improves numerical stability through two key components: (i) the Adaptive Block Lanczos (ABLE) method, which maintains biorthogonality using SVD-based stabilization, and (ii) Chebyshev filtering, which enhances spectral separation via iterative polynomial filtering. Numerical experiments on dense and sparse test problems confirm the effectiveness of the ABLE-Chebyshev algorithm, showing significantly improved accuracy and convergence compared to standard block Lanczos, especially in challenging spectral regimes with clustered or tightly packed eigenvalues.</p>

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Efficient computation of dominant eigenvalues using adaptive block Lanczos with Chebyshev filtering

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Mohamed El Guide,
  • Khalide Jbilou,
  • Kamal Lachhab

摘要

We present an efficient method for computing dominant eigenvalues of large, nonsymmetric, diagonalizable matrices based on an adaptive block Lanczos algorithm combined with Chebyshev polynomial filtering. The proposed approach improves numerical stability through two key components: (i) the Adaptive Block Lanczos (ABLE) method, which maintains biorthogonality using SVD-based stabilization, and (ii) Chebyshev filtering, which enhances spectral separation via iterative polynomial filtering. Numerical experiments on dense and sparse test problems confirm the effectiveness of the ABLE-Chebyshev algorithm, showing significantly improved accuracy and convergence compared to standard block Lanczos, especially in challenging spectral regimes with clustered or tightly packed eigenvalues.