A new algorithm for solution of resistive networks involving diodes

The solution of electric network problems by various algorithms such as for example Newton's method is often hampered by the presence of physical diodes with steeply rising exponential characteristics which cause overflow and slow convergence during numerical computation. In this paper we propose and analyze an algorithm which bypasses these difficulties by successively approximating the steep diode characteristics by smoother exponential functions. The algorithm may be modified to be used in the presence of ideal diodes and is related to penalty and multiplier methods for constrained minimization and Davidenko's method for solving certain ill-conditioned systems of nonlinear equations.