1. A method utilizing a modeling system for producing a digital pre-distortion processing device (PDPD) for a non-linear system, comprising: receiving, at an input of the modeling system, a physical electronic signal from said non-linear system by applying a set of input samples x(n) to said non-linear system and providing an output y(n) of said non-linear system as the physical electronic signal at the input of the modeling system; storing non-transitory information related to the physical electronic signal in a non-volatile memory of the modeling system; directly computing, utilizing a processor of the modeling system, parameters Φ of a non-linear system memory model for said non-linear system from the information related to said physical electronic signal, wherein said memory model comprises one or more look-up tables of said PDPD having linear interpolation and wherein said parameters Φ produce a substantially minimum mean square error; and producing said PDPD by writing, at an output of the modeling system, said parameters Φ for storage as entries in said one or more look-up tables to a memory of said PDPD to form the processor that provides digital pre-distortion in the non-linear system; wherein: said parameters Φ are computed using a tri-diagonal auto correlation matrix; and said directly computing of said parameters Φ to produce a substantially minimum mean square error comprises finding a minimum of a cost function given by: 
 Φ=( U T U ) −1 ·U T Y; wherein: Φ is a vector comprised of model parameters comprising entries for the look-up tables; T indicates a Transpose matrix; U is of a form: U = [ 0 … 0 u 0 1 - u 0 0 … 0 0 u 1 1 - u 1 0 0 0 … 0 ⋮ ⋮ 0 0 … 0 0 u N - 1 1 - u N - 1 0 ] ; u m,n =Λ(X n −mδ); Λ is a triangular basis function; m is a row of U; n is a column of U; and x n is an output of said non-linear system, given y n as an input.