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It can be shown that the interpolation matrix in the above equation is non-singular, if the points <math>\mathbf x_i</math> are distinct, and thus the weights <math>w</math> can be solved by simple linear algebra:
:<math>\mathbf{w} = \mathbf{G}^{-1} \mathbf{b}</math>
where <math>G = (g_{ij})</math>.
===Function approximation===
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