The Toeplitz matrix: Its occurrence in antenna problems and a rapid inversion algorithm

A special form of the Toeplitz matrix which frequently occurs in the numerical solution of antenna analysis and synthesis problems is discussed. Specific examples are presented illustrating its occurrence in the solution of the integral equation for a thin cylindrical antenna and in the theory of arrays. A matrix inversion algorithm is presented which, by exploiting the unique symmetry properties of the Toeplitz matrix, specifies the inverse matrix elements in terms of recurrence relationships. In this way computational time is proportional to the square of the matrix order rather than the cube as is the case with a general algorithm.