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Iterative Solution of Saddle-Point Systems from Radial Basis Function (RBF) Interpolation

Scattered data interpolation using conditionally positive definite radial basis functions typically leads to large, dense, and indefinite systems of saddle-point type. Due to ill-conditioning, the iterative solution of these systems requires an effective preconditioner. Using the technique of $\mathcal{H}$-matrices, we propose, analyze, and compare two preconditioning approaches: transformation of the indefinite into a positive definite system using either Lagrangian augmentation or the nullspace method combined with subsequent $\mathcal{H}$-Cholesky preconditioning. Numerical tests support the theoretical condition number estimates and illustrate the performance of the proposed preconditioners which are suitable for problems with up to $N \approx 40000$ centers in two or three spatial dimensions.

راه‌حل تکراری سیستم‌های نقطه - سدل از تعامل تابع بیماری شعاعی (RBF)

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