Basic HTML version of Foils prepared March 15 00

Foil 9 Convergence of Jacobi in One Dimension

From Collection of Extra Foils for CPS615 PDE Iterative Solution Discussion CPS615 Spring Semester 00 -- March 00. by Geoffrey C. Fox
For Jacobi the iteration matrix G = M-1N takes the form D-1(A-D) where D is diagonal part of A
One can calculate analytically the eigenvalues in this case and find that if one has N gridpoints, largest eigenvalue of G is
Thus if one requires an error of 10-6, then the number of iterations is given by a dreadfully large number K where

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