We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving almost sure 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.
Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
Sommariva A.;Vianello M.
2025
Abstract
We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving almost sure 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.
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