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REPRESENTATION OF FRESNEL FUNCTIONS IN CONTINUED FRACTIONS
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The goal of this paper is to provide an efficient method for computing the Fresnel functions by using the continued fractions with matrix arguments. We notice that the computation of these functions imposes many difficulties. Furthermore, we give some numerical examples which illustrated the theoretical results
Abstract
The goal of this paper is to provide an efficient method for computing the Fresnel functions by using the continued fractions with matrix arguments. We notice that the computation of these functions imposes many difficulties. Furthermore, we give some numerical examples which illustrated the theoretical results
참고문헌 (13)
- S. Albeverio, "Generalized Fresnel integrals", Bulletin des Sciences Math´ematiques, 129(1), pp.1~23 (2005)
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- G. H. Golub, "Matrix Computations" (1996), University Press
- T. L. Hayden, "Continued fractions in Banach spaces", Rocky Mtn. J.Math, 4, pp.367~369 (1974)
- W. B. Jons, "Continued Fractions, Analytic Theory and Applications" (1980), Addison-Westly Publishing Company
- A. N. Khovanski, "The applications of continued fractions and their Generalisation to problems in approximation theory" (1963), Noordhoff
- L. Lorentzen, "Continued fractions with applications" (1992), Elsevier Science Publishers
- G. J. Murphy, "C∗-Algebras and operators theory" (1990), Academic press, INC Harcourt Brace Jovanovich
- M. Raıssouli, "Convergence for matrix continued fractions", Linear Algebra Appl., 320, pp.115~129 (2000)
- N. Negoescu, "Convergence theorems on noncommutative continued fractions", Rev. Anal. Num´er. Theorie Approx, 5, pp.165~180 (1977)
- M. Sandoval-Hermandez, "Approximations of Fresnel Integrals with applications to Diffraction Problems", Mathematical Problems in Engineering, pp.1~31 (2018)[DOI]
- H. Zhao, "Matrix-valued continued fractions", Jornal of Approximation Theory, 120, pp.136~152 (2003)
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