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A method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programming
Cimprič, Jaka
N. Z. Shor, J. B. Lasserre in P. A. Parrilo so razvili metodo za računanje globalnih minimumov polinomov v več spremenljivkah, ki temelji na semidefinitnem programiranju. Namen tega članka je ...razširiti varianto te metode na nekomutativne simetrične polinome v spremenljivkah ▫$X$▫ in ▫$Y$▫, ki zadoščata relacijam ▫$YX-XY = 1$▫, ▫$X^\ast = X$▫ in ▫$Y^\ast = -Y$▫. Globalni minimumi takih polinomov se ujemajo z minimumom spektra pripadajočih diferencialnih operatorjev. Obravavamo tudi, kako lahko izkoristimo simetrije in majhno število neničelnih koeficientov. Vključenih je več numeričnih eksperimentov. V zadnjem razdelku pojasnimo zvezo med našo teorijo in nekomutativno realno algebraično geometrijo.
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