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Nonsingularity of unsymmetric Kansa matrices: Random collocation by MultiQuadrics and Inverse MultiQuadrics

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  • Cavoretto, R.
  • De Rossi, A.
  • Dell’Accio, F.
  • Sommariva, A.
  • Vianello, M.

Abstract

Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the collocation points are chosen by any continuous random distribution in the domain interior and arbitrarily on its boundary.

Suggested Citation

  • Cavoretto, R. & De Rossi, A. & Dell’Accio, F. & Sommariva, A. & Vianello, M., 2025. "Nonsingularity of unsymmetric Kansa matrices: Random collocation by MultiQuadrics and Inverse MultiQuadrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 390-395.
    • Handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:390-395
    DOI: 10.1016/j.matcom.2025.03.005
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    References listed on IDEAS

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    1. Cavoretto, Roberto & De Rossi, Alessandra, 2020. "Adaptive procedures for meshfree RBF unsymmetric and symmetric collocation methods," Applied Mathematics and Computation, Elsevier, vol. 382(C).
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