Demiralp, Metin; Tuna, Süha Zero interval limit perturbation expansion for the spectral entities of Hilbert-Schmidt operators combined with most dominant spectral component extraction: formulation and certain technicalities. (English) Zbl 1373.65093 J. Math. Chem. 55, No. 6, 1253-1277 (2017). Summary: A perturbation-expansion-at-zero-interval-limit based numeric al algorithm to calculate the eigenpairs of Hilbert-Schmidt integral operators having symmetric kernels is developed in the present work. We have developed the perturbation expansion only for the most dominant eigenvalue and relevant eigenfunction. The less important eigenpairs have been determined by using the most dominant spectral component extraction recursively over the kernel restrictions. The main lines of the formulation and certain related technicalities are presented here. The confirmation of the presented theory via certain illustrative implementations and the convergence discussion for the obtained perturbation series as well as the numerical comparison with some mostly considered methods are given in the next companion of this paper. Cited in 1 ReviewCited in 2 Documents MSC: 65R20 Numerical methods for integral equations 45C05 Eigenvalue problems for integral equations 45P05 Integral operators 47A10 Spectrum, resolvent 47B07 Linear operators defined by compactness properties 47G10 Integral operators Keywords:Hilbert-Schmidt integral operators; perturbation expansions; eigenvalues; eigenfunctions; singular value decomposition for continuous functions; most dominant spectral component extraction Software:MuPAD PDFBibTeX XMLCite \textit{M. Demiralp} and \textit{S. Tuna}, J. Math. Chem. 55, No. 6, 1253--1277 (2017; Zbl 1373.65093) Full Text: DOI References: [1] Gan, HH; Eu, BC, No article title, J. Chem. Phys. 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