The characteristic basis function method (CBFM) has been hybridized with the adaptive cross approximation (ACA) algorithm to construct a reduced matrix equation in a time-efficient manner and to solve electrically large antenna array problems in-core, with a solve time orders of magnitude less than those in the conventional methods. Various numerical examples are presented that demonstrate that the proposed method has a very good accuracy, computational efficiency and reduced memory storage requirement. Specifically, we analyze large 1-D and 2-D arrays of electrically interconnected tapered slot antennas (TSAs). The entire computational domain is subdivided into many smaller subdomains, each of which supports a set of characteristic basis functions (CBFs). We also present a novel scheme for generating the CBFs that do not conform to the edge condition at the truncated edge of each subdomain, and provide a minor overlap between the CBFs in adjacent subdomains. As a result, the CBFs preserve the continuity of the surface current across the subdomain interfaces, thereby circumventing the need to use separate ldquoconnectionrdquo basis functions.