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このアイテムの引用には次の識別子を使用してください: http://hdl.handle.net/10445/8042

タイトル: A new method of convergence acceleration of series expansion for analytic functions in the complex domain
著者: Murashige, Sunao
Tanaka, Ken'ichiro
アブストラクト: This paper proposes a new method of convergence acceleration of series expansion of complex functions which are analytic on and inside the unit circle in the complex plane. This class of complex functions may have some singularities outside the unit circle, which dominate convergence of series expansion. In the proposed method, the singular points are moved away from the origin using conformal mapping, and the function is expanded using a sequence of polynomials orthogonalized on the boundary of the mapped complex domain. The decay rate of coefficients of the orthogonal polynomial expansion can be related to the convergence region in a similar form to the Cauchy–Hadamard formula for power series. Using this relation, we quantitatively evaluate and maximize the convergence rate of the improved series. Numerical examples demonstrate that the proposed method is effective for slow convergent series, and may converge faster than Padé approximants.
研究業績種別: 原著論文/Original Paper
資料種別: Journal Article
査読有無: あり/yes
単著共著: 共著/joint
発表雑誌名,発表学会名など: Japan Journal of Industrial and Applied Mathematics
巻: 32
号: 1
開始ページ: 95
終了ページ: 117
年月日: 2015年3月
出版社: Springer
出現コレクション:田中 健一郎





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