$$
y(\mathbf) \, = \, \sum_^N w_i \, \phi(||\mathbf - \mathbf_i||) +
\mathbf^T \, \begin 1 \\ \mathbf \end

$$
\begin
\phi(r) = \begin
r^k & \mbox k=1,3,5,\dots, \\
r^k \ln(r) & \mbox k=2,4,6,\dots
\end \\()
r = ||\mathbf - \mathbf_i||_2
= \sqrt_i)^T \, (\mathbf - \mathbf_i) }
\end

$$
\phi(r) = \begin
r^ \ln(r^r) & \mbox r < 1 \\
r^k \ln(r) & \mbox r \ge 1
\end

$$
0 = \sum_^N w_i, \;\; 0 = \sum_^N w_i \, c_ \;\;\; (j=1,2,...,nx)

$$
\begin
\mathbf & \mathbf^T \\
\mathbf & \mathbf \end
\;
\begin
\mathbf \\
\mathbf
\end \; = \;
\begin
\mathbf \\
\mathbf
\end\;\;\;\;

$$
A_ = \phi(||\mathbf_i - \mathbf_j||), \;\;\;
\mathbf =
\begin
1 & 1 & \cdots & 1 \\
\mathbf_1 & \mathbf_2 & \cdots & \mathbf_
\end, \;\;\;
\mathbf = (y_2, \cdots, y_N )^T