A Numerical Method for Solving Ill-Conditioned Equation Systems Arising from Radial Basis Functions

Continuously differentiable radial basis functions (C∞-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices full and can become very ill- conditioned. Similarly, Hilbert Vandermonde have ill-conditioned. The difference between a matrix generated by C∞-RBFs for partial differential or integral equations systems is that sensitive to small changes in adjustable parameters. These parameters affect condition number solution accuracy. error terrain has many local global maxima minima. To find stable accurate numerical solutions linear equation systems, this study proposes hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) minimize accumulation rounding errors. In future, algorithm execute faster using preconditioners implemented on massively parallel computers.