near the boundary $\operatorname{\partial\Omega}$. As before, if $\gamma=\gamma_0\neq1$ near $\operatorname{\partial\Omega}$, the problem can be scaled.

Note that if the admittivity is purely real-valued, then simplifications to the first-order system method exist \[[@Brown1997], [@Knudsen2003], [@Knudsen2002]\].

Computational Details {#sec:CompDetails}
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Here we present a self-contained summary of the implementation of [*‘Approach 2’*]{} for complex-valued conductivities. For numerical implementations of the D-bar method for real-valued conductivities see \[[@Mueller2012], [@DeAngelo2010]\] and for [*‘Approach 1’*]{} for complex-valued conductivities see \[[@Hamilton2012; @Hamilton2013]\].

We present the numerical solution method based on trigonometric current patterns, however any set of $L-1$ linearly independent measurements (for a system with $L$ electrodes) can be transformed via a change of basis to synthesize the measurements that would have occurred if the trigonometric current patterns presented here had been applied.

To form the discrete approximation $\mathbf{R}_\gamma$ to the ND map $\mathcal{R}_\gamma$ we use an inner product of the measured currents and voltages on the electrodes as in \[[@Isaacson2004]\]. Let $\Phi^j_\ell$ denote the current on the $\ell$-th electrode arising from the $j$-th trigonometric current pattern: $$\label{eq:trigCPs}
\Phi^j_\ell=\Phi(\ell,j):=\begin{cases}
A\cos(j\theta_\ell), & 1\leq j\leq \frac{L}{2},\;\;1\leq \ell\leq L\\
A\sin((\frac{L}{2}-j)\theta_\ell) & \frac{L}{2}+1\leq j\leq L-1,\;\;1\leq \ell\leq L,
\end{cases}$$ where $A$ is the amplitude of the applied current, and $V^j_\ell$ denotes 