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Symbolic-Numerical Algorithm for Large Scale Calculations the Orthonormal \(\mathrm {SU(3)}\) BM Basis

  • A. Deveikis
  • A. A. GusevEmail author
  • V. P. Gerdt
  • S. I. Vinitsky
  • A. Góźdź
  • A. Pȩdrak
  • Č. Burdik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11661)

Abstract

In this paper we proposed a new symbolic, non-standard recursive and fast orthonormalization procedure of linearly independent vectors but as in other approaches not orthonormal based on the Gram-Schmidt orthonormalization algorithm. Our adaptation of the Gram-Schmidt orthonormalization procedure provide simple analytic formulas for the \(\mathrm {SU(3)}\) Bargmann-Moshinsky basis orthonormalization coefficients and do not involve any square root operation on the expressions coming from the previous iterative computation steps. This distinct features of the proposed orthonormalization algorithm may make the large scale symbolic calculations feasible. We demonstrate efficiency of our procedure by benchmark large-scale calculations of the non-canonical BM basis with the highest weight vectors of \(\mathrm {SO(3)}\) irreducible representations.

Notes

Acknowledgements

The work was partially supported by the Bogoliubov-Infeld program, Votruba-Blokhintsev program, the RUDN University Program 5-100 and grant of Plenipotentiary of the Republic of Kazakhstan in JINR. AD is grateful to Prof. A. Góźdź for hospitality during visits in Institute of Physics, Maria Curie-Skłodowska University (UMCS).

The authors thank the both referees for their useful comments, remarks and suggestions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • A. Deveikis
    • 1
  • A. A. Gusev
    • 2
    Email author
  • V. P. Gerdt
    • 2
  • S. I. Vinitsky
    • 2
    • 3
  • A. Góźdź
    • 4
  • A. Pȩdrak
    • 5
  • Č. Burdik
    • 6
  1. 1.Department of Applied InformaticsVytautas Magnus UniversityKaunasLithuania
  2. 2.Joint Institute for Nuclear ResearchDubnaRussia
  3. 3.RUDN UniversityMoscowRussia
  4. 4.Institute of PhysicsMaria Curie-Skłodowska UniversityLublinPoland
  5. 5.National Centre for Nuclear ResearchWarsawPoland
  6. 6.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityPragueCzech Republic

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