1. A system for a conjugate gradient iterative linear solver that calculates the solution to a matrix equation, the system comprising: a field programmable gate array (FPGA), including a plurality of configurable logic elements and a plurality of configurable storage elements; a plurality of gamma processing elements formed from configurable logic elements and configurable storage elements, and configured to receive an A-matrix and a direction vector, and to calculate a q-vector and a gamma scalar; a plurality of direction vector processing elements formed from configurable logic elements and configurable storage elements, and configured to receive a beta scalar and a residual vector, and to calculate the direction vector; a plurality of x-vector processing elements formed from configurable logic elements and configurable storage elements, and configured to receive an alpha scalar, the direction vector, and the q-vector, and to calculate an x-vector and the residual vector; an alpha processing element formed from configurable logic elements and configurable storage elements, and configured to receive the gamma scalar and a delta scalar, and to calculate the alpha scalar; and a beta processing element formed from configurable logic elements and configurable storage elements, and configured to receive the residual vector, and to calculate the delta scalar and the beta scalar.