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.
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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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Deveikis, A. et al. (2019). Symbolic-Numerical Algorithm for Large Scale Calculations the Orthonormal \(\mathrm {SU(3)}\) BM Basis. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_7
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