Sparse preconditioners of Gram’s matrices in the conjugate gradient method

  • G. Moreaux
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 121)


When harmonic spherical splines are used to interpolate and predict discretely given data we are confronted with the problem of solving symmetric positive-definite systems involving as many equations as the number of data Due to harmonicity, these systems are full and thus iterative methods like the conjugate gradient method should be prefered to direct methods such as the Cholesky factorization for large data sets. In order to speed-up classic iterative solvers, we present a class of sparse symmetric positive definite preconditioners which hold foe any minimization norm, i.e. for any harmonic reproducing kernel, and for any data distribution. Numerical results are shown and demonstrate the efficiency of our method


Reproducing kernels positive definite functions iterative methods 


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Copyright information

© SPringer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • G. Moreaux
    • 1
  1. 1.Department of GeophysicsUniversity of CopenhagenCopenhagen ODenmark

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