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Implications of using norm_1 (L1 norm) with iterative solvers?

tario
2017-08-19
2017-08-19
  • tario

    tario - 2017-08-19

    Hello,

    I want to solve problems in connection with an engineering/physics application using the ViennaCL iterative solvers.

    The application uses the L1 normfactor while the ViennaCL linear solvers use norm_2. Websearch
    tells me that L1 is more suitable to solve problems with sparse matrices and my matrices are all sparse.

    It looks to me as if norm_2 is "hardcoded" in the solver source codes. Why?

    Is it possible to "set()" the norm_1 without changing the source code?

    T.

     
  • Karl Rupp

    Karl Rupp - 2017-08-19

    Hi Tario,
    ViennaCL uses either the 2-norm or the energy norm. These norms are indeed hardcoded for the time being. Why do you think that the 1-norm is more natural?
    Best regards,
    Karli

     
  • tario

    tario - 2017-08-20

    Hi Karli,
    I don't have an opinion on that, it's a necissity to think about it as the physics/CFD application uses the L1 norm and e.g. according to http://www.chioka.in/differences-between-the-l1-norm-and-the-l2-norm-least-absolute-deviations-and-least-squares/ L1 is supposed to be more suitable for sparse matrix problems.

    Technical problems could arise with a "monitoring" function of the application which usually gets as a return/input from the solver the current residual / L1 norm. Apparently adjustments were needed when using ViennaCL 1.2 a few years ago to make it work but I don't have the source code or any details. I'll see, whether there are implications when the interface is up and running.

    T.

     
  • Karl Rupp

    Karl Rupp - 2017-08-22

    Hi Tario,
    well, engineering applications often minimize a certain energy functional, so it's also natural to monitor that. It is natural for Krylov solvers to monitor convergence in such an energy-norm, typically of the form (x,Ax).

    Btw: You can always specify your own monitor function, in which you compute the L1-norm.

    Best regards,
    Karli

     

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