Convergence of Conjugate Gradient in Diagonalized Form

• We want for all i

• But

  

• We order eigenvalues

• If non zero and reasonably big

• Then

  

• But other i>1 are largely unchanged if eigenvalues because as is multiplied by (when ) on going from iteration to k
  

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  Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu