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Jacobi Iteration

  1. Apr 22, 2010 #1
    1. The problem statement, all variables and given/known data

    consider the systems of equations
    2x1 - x2 = 1
    -31 + 4x2 =11

    a) determine the ixact solution?

    b)apply jacobi iteration.Does the matrix C satisfy the required condition?

    c)starting with x(0) =( [tex]\stackrel{1}{1}[/tex] ) calculate x(1) and x(2) and the prior error bound for x(2)

    d)how many iterations will suffice to get within 0.001 of the solution?

    a) grand 3 and 5
    b) it clearly satisfies the condition as off diagonals < diagonals
    c) so did it out got
    x(0) = ( [tex]\stackrel{1}{14/4}[/tex] )

    x(1) = ( [tex]\stackrel{18/8}{14/4}[/tex] )

    x(2) = ( [tex]\stackrel{18/8}{71/16}[/tex] )

    but now im not sure what is meant by prior error bound, compare with the actual error?

    d) do i just keep doing it out till i get within .001? (aghhhhh)
     
  2. jcsd
  3. Apr 22, 2010 #2
    It's the error estimate that can be obtained before the actual iteration's calculus. There's an expression for it in terms of the matrixes.

    No. You use the expression for the a priori error (it depends on n) to find n.
     
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