The kernel polynomial method based on Jacobi polynomials

I.O. Raikov and Y.M. Beltukov

Applied Mathematics and Computation, 2025, vol. 490, issue C

Abstract: The kernel polynomial method based on Jacobi polynomials Pn(α,β)(x) is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are calculated. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials. For α=±1/2, β=±1/2 (Chebyshev polynomials of the first to fourth kinds), explicit trigonometric expressions for the damping factors are obtained. The resulting algorithm can be easily introduced into existing implementations of the kernel polynomial method.

Keywords: Kernel polynomial method; Jacobi polynomials; Damping factors; Non-negative kernels (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006684

DOI: 10.1016/j.amc.2024.129207

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