- #1

sigh1342

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## Homework Statement

show SOR iteration method converges for the system.

$$6x+4y+2z=11$$

$$4x+7y+4z=3$$

$$2x+4y+5=-3$$

## Homework Equations

if the coeff. matrix is positive definite matrix and 0≤ω≤2. Then SOR converge for any initial guess.

Or if $$ρ(T_{ω})$$≥|ω-1|, then SOR converge for any initial guess.ρ(T) means the largest magnitude of all eigenvalue of T.$$T_{ω}=(I − ωL)^{-1} ((1 − ω)I + ωU)$$

Or any norm of $$T_{ω} <1 $$ Then SOR converge for any initial guess

## The Attempt at a Solution

I found that the coeff. matrix is not positive definite matrix . and the ρ(T) is hard to find .

Any other method ? Or what I miss. Thanks you