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Alternative Tikhonov-Type Regularization for the Calderón Inverse Conductivity Problem — arXiv:2611.01034

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01034
License (as archived): CC0-1.0
Archived: 2026-11-03T11:35:38.062Z
SHA-256 of the archived text: 1671eb97a56025c1cb9a9a04a97623d3649b227d9a25602fee380f84c2c2a567
Stable URL of this page: https://metraipolis.com/documento/dc_31e2dfd68283

How to cite

Alternative Tikhonov-Type Regularization for the Calderón Inverse Conductivity Problem — arXiv:2611.01034 — arXiv (en), https://arxiv.org/abs/2611.01034 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_31e2dfd68283 (Metraipolis archive dc_31e2dfd68283, sha256 1671eb97a56025c1cb9a9a04a97623d3649b227d9a25602fee380f84c2c2a567)

BibTeX

@misc{dc31e2dfd68283,
  title = {Alternative Tikhonov-Type Regularization for the Calderón Inverse Conductivity Problem — arXiv:2611.01034},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01034},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_31e2dfd68283; sha256 1671eb97a56025c1cb9a9a04a97623d3649b227d9a25602fee380f84c2c2a567},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01034. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper investigates the application of two regularization methods, classical Tikhonov and Alternative Tikhonov regularization, to the Calderón inverse conductivity problem. We develop an iterative reconstruction scheme based on linearizing the Dirichlet-to-Neumann map and approximating conductivity updates using Gaussian basis functions. The resulting linear systems are solved using both regularization methods, with particular attention given to the derivation and numerical implementation of Alternative Tikhonov regularization. We compare the performance of these methods through numerical experiments on a synthetic conductivity containing two localized regions of differing conductivity. A total of 666 reconstruction tests are performed across varying regularization parameters, damping factors, and iteration counts. The lowest relative reconstruction errors obtained are 0.064730 for Alternative Tikhonov and 0.065173 for classical Tikhonov regularization. Although both methods produce comparable reconstructions, Alternative Tikhonov achieves the lowest observed error. The results demonstrate the effectiveness of both approaches within the proposed reconstruction scheme and motivate further investigation into parameter selection, numerical stability, and reconstruction accuracy.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2611.01034 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:05:07.199Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).