An algebraic method for identification of dipoles and quadrupoles

This paper proposes an algebraic algorithm for reconstruction of dipole–quadrupole positions and moments in 2D space from the boundary measurements of the potential without providing an initial parameter guess or iterative computing forward solutions. A system of second-order equations is derived for the elementary symmetric polynomials of the pole positions. An algorithm to transform them into a triangular form is shown so that the pole positions are obtained algebraically. Numerical simulations are conducted to verify the algorithm.