Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
<|reference_start|>Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers: We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed boundary conditions. We also show some numerical tests, where the fictitious centers are local random perturbations of predetermined collocation points.<|reference_end|>
@article{mohammadi2024unisolvence,
    title={Unisolvence of Kansa collocation for elliptic equations by polyharmonic
  splines with random fictitious centers},
    author={Maryam Mohammadi, Alvise Sommariva, and Marco Vianello},
    journal={arXiv preprint arXiv:2410.03279},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.03279},
    primaryClass={math.NA cs.NA math.AP}
}