Skip to content
DraconiticResearch
Search Sources API
189,280 studies31 sourcesUpdated 51 min ago
PreprintCC BY-NC-ND 4.0arXiv

High-order guaranteed lower bounds for the Schrödinger eigenvalue problem

  • Benedikt Gräßle
  • Moritz Hauck
  • Yizhou Liang
Open at sourcePDFDOICite

Abstract

We compute unconditional guaranteed lower eigenvalue bounds for Schrödinger operators using a modified hybrid high-order method with built-in correction for the potential defect. The method assumes exact numerical integration and allows possibly unbounded potentials in Lp for p>n/2 and p≥2 on general polyhedral domains. We prove that the high-order correction preserves optimal a priori convergence orders, and derive reliable and efficient a posteriori error estimators. Numerical experiments provide striking evidence of optimal high-order convergence rates of the adaptive algorithm.

Related

  1. Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds
    Eduard Stefanescu
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Lower bounds for the magnitude of the minimum eigenvalue of graphs with applications to MaxCut and Chowla's cosine problem
    Fredy Yip
    arXivPreprintarXiv licenceFull textAnalysis & PDEsCombinatorics & discrete mathematicsarXiv
  3. A Modified Direct Eigenvalue Swapping Algorithm with Guaranteed Stability
    Meiyue Shao, Rentao Xu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Guaranteed wave-speed bounds for the compressible Euler equations with a composite equation of state
    Nicolas Favrie, Matthias Maier
    arXivPreprintarXiv licenceFull textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  5. Non-Fragile Guaranteed Cost Control for Uncertain Fractional Delay Systems of Variable Order with Time-Varying Control Input Delays: A Possibly Stability Analysis
    Alireza Alfi, Zahra Sadat Aghayan, António M. Lopes
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref

Cite

BibTeXRIS
BibTeX
@misc{graßle2026highorder,
  title = {{High-order guaranteed lower bounds for the Schrödinger eigenvalue problem}},
  author = {Benedikt Gräßle and Moritz Hauck and Yizhou Liang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03567},
  eprint = {2611.03567},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03567},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - High-order guaranteed lower bounds for the Schrödinger eigenvalue problem
AU  - Benedikt Gräßle
AU  - Moritz Hauck
AU  - Yizhou Liang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03567
UR  - https://arxiv.org/abs/2611.03567
AB  - We compute unconditional guaranteed lower eigenvalue bounds for Schrödinger operators using a modified hybrid high-order method with built-in correction for the potential defect. The method assumes exact numerical integration and allows possibly unbounded potentials in L^p for p>n/2 and p≥2 on general polyhedral domains. We prove that the high-order correction preserves optimal a priori convergence orders, and derive reliable and efficient a posteriori error estimators. Numerical experiments provide striking evidence of optimal high-order convergence rates of the adaptive algorithm.
ER  -