The Best Constant for Error in Orthogonal Projection onto Finite-dimensional Subspaces of Abstract Hilbert Spaces

DOI
  • Takahashi Munehisa
    Graduate School of Information and Computer Science, Chiba Institute of Technology
  • Sekine Kouta
    Department of Computer Science, Chiba Institute of Technology
  • Mizuguchi Makoto
    Department of Information and System Engineering, Chuo University

Bibliographic Information

Other Title
  • 抽象的なHilbert空間の有限次元部分空間への直交射影の誤差に対する最良定数

Abstract

<p>Abstract. The prior error evaluation of the Galerkin method for the Poisson equation is expressed by the projection, and the constants have been studied to evaluate the convergence and error of the approximate solution. This paper considers error constants for orthogonal projections on finite-dimensional subspaces of the abstract Hilbert space. By proving the converse of the Aubin-Nitsche technique without restricting compactness or the basis, we show that the constants satisfying two inequalities are equal. Next, it is also shown that the best error constant under the compactness assumption is the smallest eigenvalue of the eigenvalue problem.</p>

Journal

Keywords

Details 詳細情報について

  • CRID
    1390018120873739264
  • DOI
    10.11540/jsiamt.34.1_19
  • ISSN
    24240982
  • Text Lang
    ja
  • Data Source
    • JaLC
  • Abstract License Flag
    Disallowed

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