数学季刊 ›› 1999, Vol. 14 ›› Issue (3): 96-102.

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关于无穷维算子的有限维最佳逼近

  

  1. Department of Mathematics,Shanxi Teacher’s University,Linfen,041004

  • 收稿日期:1996-04-24 出版日期:1999-09-30 发布日期:2024-09-18

On the Finite-dimensional Optimal Approximations to the Infinite dimensional Linear Operators

  1. Department of Mathematics,Shanxi Teacher’s University,Linfen,041004
  • Received:1996-04-24 Online:1999-09-30 Published:2024-09-18

摘要: A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.

关键词:  , Hilbert space;linear operator;optimal approximation

Abstract: A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.

Key words:  , Hilbert space;linear operator;optimal approximation

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