# Jacobi Iteration

1. Apr 22, 2010

### gtfitzpatrick

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) =( $$\stackrel{1}{1}$$ ) 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) = ( $$\stackrel{1}{14/4}$$ )

x(1) = ( $$\stackrel{18/8}{14/4}$$ )

x(2) = ( $$\stackrel{18/8}{71/16}$$ )

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. Apr 22, 2010

### JSuarez

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.