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

Source: [Efficient Computation of Dominant Eigenvalues Using Adaptive Block Lanczos with Chebyshev Filtering](<https://www.sota2.com/research/paper/68fa5e091e209131ce9ded41>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T18:33:57.677Z

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

Published: 2025-08-11T21:58:21.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2508.08495>)

[PDF](<https://arxiv.org/pdf/2508.08495.pdf>)