Basic HTML version of Foils prepared 8 November 1995

Foil 40 Jacobi Iteration Eigenvalues as a function of Over Relaxation Parameter

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox
lJOR|max(w) = 1 - ew
  • This is decreased in absolute value for w > 1, increased for w < 1
lJOR|min(w) = 1+ we - 2w
  • This is just the opposite
  • Increased for w > 1, decreased for w < 1
The best value of w is w = 1 i.e. Best is Original Jacobi iteration as one must minimize the maximum over all values of eigenvalue moduli |l| and for Jacobi one canNOT use overrelaxation

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