Geodesic
Renormalization group approach to function approximation and to improving subsequent approximations
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 243-261

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We establish a relation between bijective functions and renormalization group transformations and find their renormalization group invariants. For these functions, taking into account that they are globally one-to-one, we propose several improved approximations (compared with the power series expansion) based on this relation. We propose using the obtained approximations to improve the subsequent approximations of physical quantities obtained, in particular, by one of the main calculation techniques in theoretical physics, i.e., by perturbation theory. We illustrate the effectiveness of the renormalization group approximation with several examples: renormalization group approximations of several analytic functions and calculation of the nonharmonic oscillator ground-state energy. We also generalize our approach to the case of set maps, both continuous and discrete.
Keywords: renormalization group, bijective function, approximation, improved approximation.
Mots-clés : invariant, perturbation method 
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     author = {G. N. Nikolaev},
     title = {Renormalization group approach to function approximation and to improving subsequent approximations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {243--261},
     publisher = {mathdoc},
     volume = {164},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a5/}
}
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G. N. Nikolaev. Renormalization group approach to function approximation and to improving subsequent approximations. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 243-261. http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a5/