Gauss seidel method of convergence

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SUMMARY

The discussion centers on the Gauss-Seidel method and its convergence criteria, specifically the spectral radius. It is established that the spectral radius must be a single value, and convergence occurs when this value is less than one. The user initially presented multiple spectral radius values (0.45, 2.15, and 0), leading to confusion regarding convergence. The conclusion is that only one spectral radius value is relevant for determining convergence, and it must be less than one.

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  • Understanding of the Gauss-Seidel method for solving linear systems
  • Knowledge of spectral radius in numerical analysis
  • Familiarity with convergence criteria in iterative methods
  • Basic linear algebra concepts
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lavster
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hi,

im trying to calculate the spectral radius (gauss seidel method) to test whether or not its converges. i no that if the modulus is less than one it converges. however, my answer gives a mixture of solutions which are above and below one - 0.45 and 2.15 and 0. so is this divergent or convergent? does all three need to be below 1 in order for it to converge?

thanks
 
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I can't make heads or tails of your question, but the spectral radius is one number only.
 
yeah, i was confused. but i get it now :)
 

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