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Which vectorial norm should I use?

  1. Dec 4, 2015 #1
    I am to study how fast an iterative method for nonlinear system of equations converges to a certain root and found out that I can evaluate my rate of convergence by using the following formula: ##r^{(k)}=\frac{||x^{(k+1)}-x^{(k)}||_V}{||x^{(k)}-x^{(k-1)}||_V}##. My question is which vectorial norm should I use? ##||.||_{\infty}##? ##||.||_1##? Etc... Is there any criteria in choosing them? And after getting my rate of convergence, how do I measure my order of convergence?
     
  2. jcsd
  3. Dec 5, 2015 #2

    RUber

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    Homework Helper

    I think it is common to use the infinity norm. All the norms should be related by a constant multiple anyway, so when you talk about order, it should not matter too much.
    The order of convergence is often displayed as the slope of your convergence plot on a log scale.
     
  4. Dec 6, 2015 #3

    Erland

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    Science Advisor

    If you work in a normed vector space with finite dimension, all these norms are equivalent. They give rise to the same topology.
     
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