A method or corresponding apparatus relates to a mathematical approach to efficiently search for and localize regions in a multi-dimensional signal space to enable inversion of power amplifier nonlinearities with a significant reduction in computational complexity and an efficient hardware implementation. To linearize a wideband power amplifier, an example embodiment of the present invention may represent a response of the wideband power amplifier using coefficients in a cube coefficient subspace, and search over the full multi-dimensional subspace according to an optimization criterion in order to identify a vector of cube coefficient subspace coefficients. The vector of coefficient subspace coefficients may be used to linearize the wide-band power amplifier.