Behavior of the Steepest Descent Method in Minimizing Rayleigh Quotient

• OZEKI Takashi

  school of Information Science, Japan Advanced Institute of Science and Technology

• IIJIMA Taizo

  school of Information Science, Japan Advanced Institute of Science and Technology

抄録

In this paper we discuss the limiting behavior of the search direction of the steepest descent method in minimizing the Rayleigh quotient. This minimization problem is equivalent to finding the smallest eigenvalue of a matrix. It is shown that the search direction asymptotically alternates between two directions represented by linear combinations of two eigenvectors of the matrix. This is similar to the phenomenon in minimizing the quadratic form. We also show that these eigenvectors correspond to the largest and second-smallest eigenvalues, unlike in the case of the quadratic form.

収録刊行物

• IEICE transactions on fundamentals of electronics, communications and computer sciences

  IEICE transactions on fundamentals of electronics, communications and computer sciences 80 (1), 176-182, 1997-01-25

  一般社団法人電子情報通信学会

キーワード

• numerical analysis
• steepest descent method
• Rayleigh quotient
• eigenvalue problem
• search direction

詳細情報

• CRID: 1570854177379083264
• NII論文ID: 110003207693
• NII書誌ID: AA10826239
• ISSN: 09168508
• 本文言語コード: en
• データソース種別:
  • CiNii Articles