研究者紹介システム

影山 康夫
カゲヤマ ヤスオ
大学院海事科学研究科 海事科学専攻
講師
数学関係
Last Updated :2022/09/16

研究者情報

所属

  • 【主配置】

    大学院海事科学研究科 海事科学専攻
  • 【配置】

    海洋政策科学部 海洋政策科学科, 海事科学部 海洋安全システム科学科

学位

  • 博士(工学), 名古屋大学

授業科目

ジャンル

  • 科学・技術 / 数学

コメントテーマ

  • 数値解析学
  • 関数近似

研究活動

研究キーワード

  • 数値解析学

研究分野

  • 自然科学一般 / 応用数学、統計数学
  • 自然科学一般 / 数学基礎

論文

  • 影山 康夫

    In general, zeros of a Lagrange interpolation polynomial can be calculated only numerically, but if the interpolated function is given as the form 1/(z-c) and the sampling points are equally distributed on an ellipse, then the zeros can be represented explicitly and they are also equally distributed on an ellipse of common foci. We will show this fact and prove a theorem that presents a sufficient condition for this method to be generalized.

    一般社団法人 日本応用数理学会, 2003年09月, 日本応用数理学会論文誌, 13 (3), 391 - 402, 日本語

    [査読有り]

    研究論文(学術雑誌)

  • Generalization of the Bernstein operator

    影山 康夫

    2002年12月, Analysis, Combinatorics and Computing, 265 - 274, 英語

    [査読有り]

    研究論文(国際会議プロシーディングス)

  • 影山 康夫

    In a former paper, Inoue introduced an interpolation based on a scheme in the charge simulation method, but he did not mention the problem whether the coefficient matrix derived there is regular or not. We will first point out unnaturalness of his scheme and introduce another interpolation based on so-called Murota's invariant scheme, which is a slightly modified version of Inoue's scheme. Then we will guarantee that the coefficient matrix for our scheme is always regular.

    一般社団法人 日本応用数理学会, 2001年12月, 日本応用数理学会論文誌, 11 (4), 171 - 177, 日本語

    [査読有り]

    研究論文(学術雑誌)

  • A new class of modified Bernstein operators

    Y Kageyama

    The left Bernstein quasi-interpolant operator introduced by Sablonniere is a kind of modified Bernstein operator that has good stability and convergence rate properties. However, we recently found that it is not very convenient for practical applications. Fortunately, we showed in a previous paper that there exist many operators having stability and convergence rate properties similar to those of Sablonniere's operator. In this paper, we introduce another specific class of such operators generated from the operator introduced by Stancu. We present detailed results about this class, some of which can be applied to numerical quadrature. Finally, we clarify its advantages and assert that it is more natural and more convenient, both theoretically and practically, than that of Sablonniere. Our paper, at the same time, provides several new results regarding Stancu's operator. (C) 1999 academic Press.

    ACADEMIC PRESS INC, 1999年11月, JOURNAL OF APPROXIMATION THEORY, 101 (1), 121 - 147, 英語

    [査読有り]

    研究論文(学術雑誌)

  • Generalization of the left Bernstein quasi-interpolants

    Y Kageyama

    P. Sablonniere introduced the so-called left Bernstein quasi-interpolant, and proved that the sequence of the approximating polynomials converges pointwise in high-order rate to each sufficiently smooth approximated function. On the other hand. Z.-C. Wu proved that the sequence of the norms of the operators is bounded. In this paper, we extract the essence why Sablonniere's operator exhibits good convergence and stability properties, and we clarify a sufficient condition for general operators to have similar properties. Moreover, regarding the family of the general operators, we derive detailed results about the derivatives of the approximating polynomials that estimate their uniform convergence degree, using a convenient differentiability condition on approximated functions. Our results readily imply all the preceding ones. (C) 1998 Academic Press.

    ACADEMIC PRESS INC, 1998年08月, JOURNAL OF APPROXIMATION THEORY, 94 (2), 306 - 329, 英語

    [査読有り]

    研究論文(学術雑誌)

書籍等出版物

  • 現代数理入門

    影山 康夫

    その他, 関西学院大学出版会, 2009年06月, 日本語, 「等間隔標本点を用いた多項式近似は実用にならない」という従来の常識に対し,「収束精度・数値的安定性・計算量の観点からみて実用的な近似法が存在する」という新たな知見を提示した.

    学術書

所属学協会

  • 日本応用数理学会

共同研究・競争的資金等の研究課題