A fast simple algorithm for computing the potential of charges on a line

Zydrunas Gimbutas, Nicholas F. Marshall, Vladimir Rokhlin

We present a fast method for evaluating expressions of the form $$u_j=\sum _{i=1,i\ne j}^n\frac{{\alpha }_i}{x_i-x_j},\text{for}j=1,\dots ,n,$$ where ${\alpha }_i$ are…