Resolving the problem of multiple control parameters in optimized Borel-type summation

Yukalov, V. I.; Gluzman, S.

doi:10.1007/s10910-024-01669-7

J Math Chem

2024

DOI: 10.1007/s10910-024-01669-7

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Resolving the problem of multiple control parameters in optimized Borel-type summation

V. I. Yukalov,

S. Gluzman

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2024

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Borel Summation Can Be Controlled by Critical Indices

Gluzman

2024

Symmetry

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We consider application of the self-similarity principle in approximation theory under the conditions of asymptotic scale-invariance. For the effective summation of the asymptotic series methods, an iterative Borel summation with self-similar iterated roots is applied. The approximants follow from the self-similarity considerations and behave asymptotically as a power-law satisfying the asymptotic scale invariance. Optimal conditions on convergence of the sequence of approximants are imposed through the critical indices defined from the approximants. The indices are understood as control parameters for the optimal convergence of the asymptotic series. Such interpretation of the indices leads to an overall improvement of accuracy in calculations of the indices. The statement is supported by fifteen examples from condensed matter physics, quantum mechanics and field theory.

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Borel Summation Can Be Controlled by Critical Indices

Gluzman

2024

Symmetry

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Resolving the problem of multiple control parameters in optimized Borel-type summation

Cited by 1 publication

References 46 publications

Borel Summation Can Be Controlled by Critical Indices

Borel Summation Can Be Controlled by Critical Indices

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