PreprintCC BY 4.0arXiv
Asymptotic behavior of Eckhoff's method for convergence acceleration of Dirac eigenfunction expansions
Abstract
The current paper considers the problem of recovering a vector-function on [−1,1] from a limited number of coefficients of its expansion into a series of eigenfunctions of a one-dimensional Dirac system. The Krylov--Lanczos--Eckhoff--Gottlieb acceleration method is examined in the situation when the boundary values it requires have to be computed from the generalized Fourier coefficients themselves. This leads to a 2q× 2q linear system whose matrix is a block Vandermonde matrix; its determinant and inverse are computed explicitly, and the asymptotic L2-error constant of the method is found, paralleling the classical trigonometric case.
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BibTeX
@misc{barkhudaryan2026asymptotic,
title = {{Asymptotic behavior of Eckhoff's method for convergence acceleration of Dirac eigenfunction expansions}},
author = {R. H. Barkhudaryan and G. G. Gevorkyan and L. D. Poghosyan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00895},
eprint = {2609.00895},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00895},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Asymptotic behavior of Eckhoff's method for convergence acceleration of Dirac eigenfunction expansions
AU - R. H. Barkhudaryan
AU - G. G. Gevorkyan
AU - L. D. Poghosyan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00895
UR - https://arxiv.org/abs/2609.00895
AB - The current paper considers the problem of recovering a vector-function on [−1,1] from a limited number of coefficients of its expansion into a series of eigenfunctions of a one-dimensional Dirac system. The Krylov--Lanczos--Eckhoff--Gottlieb acceleration method is examined in the situation when the boundary values it requires have to be computed from the generalized Fourier coefficients themselves. This leads to a 2q× 2q linear system whose matrix is a block Vandermonde matrix; its determinant and inverse are computed explicitly, and the asymptotic L_2-error constant of the method is found, paralleling the classical trigonometric case.
ER -