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[Author] Takashi OZEKI(1hit)

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  • Behavior of the Steepest Descent Method in Minimizing Rayleigh Quotient

    Takashi OZEKI  Taizo IIJIMA  

     
    PAPER-Numerical Analysis and Optimization

      Vol:
    E80-A No:1
      Page(s):
    176-182

    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.