Jacobi Iteration Homework: Solving System of Equations

[gtfitzpatrick]

Homework Statement

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 I am 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)

 

[JSuarez]

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

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.

do i just keep doing it out till i get within .001?

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