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Efficient Computation of Dominant Eigenvalues Using Adaptive Block Lanczos with Chebyshev Filtering

Published: August 11, 2025 | arXiv ID: 2508.08495v1

By: M. El Guide, K. Jbilou, K. Lachhab

Potential Business Impact:

Finds important numbers in big math problems faster.

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.

Page Count
18 pages

Category
Mathematics:
Numerical Analysis (Math)