Analytic Theory of Finite Asymptotic  Expansions in the Real Domain. Part II-C: Constructive Algorithms for Canonical  Factorizations and a Special Class of  Asymptotic Scales

Antonio Granata

doi:10.4236/apm.2015.58047

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Advances in Pure Mathematics > Vol.5 No.8, June 2015

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-C: Constructive Algorithms for Canonical Factorizations and a Special Class of Asymptotic Scales ()

Antonio Granata^*

Department of Mathematics and Computer Science, University of Calabria, Cosenza, Italy.

DOI: 10.4236/apm.2015.58047 PDF HTML XML 4,584 Downloads 4,869 Views Citations

Abstract

This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.

Keywords

Asymptotic Expansions, Canonical Factorizations of Disconjugate Operators, Algorithms for Canonical Factorizations, Chebyshev Asymptotic Scales

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Granata, A. (2015) Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-C: Constructive Algorithms for Canonical Factorizations and a Special Class of Asymptotic Scales. Advances in Pure Mathematics, 5, 503-526. doi: 10.4236/apm.2015.58047.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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