1. A computer processing system, comprising: an in-memory column store containing big data analytic information; a real-time analytics, interactive data exploration and application platform coupled to the in-memory column store; a communication device coupled to the real-time analytics, interactive data exploration and application platform to receive a raw input matrix A associated with the big data analytic information contained in the in-memory column store; and an adaptive tile matrix engine, coupled to the communication device, including: a memory storing processor-executable program code, and a multi-core computer processor to execute the processor-executable program code in order to cause the adaptive tile matrix engine to: load matrix A data into a temporary, unordered starting representation that contains coordinates and values for each element of matrix A, perform Z-curve ordering of matrix A and create a two-dimensional density map of matrix A by counting matrix elements that are contained in logical two-dimensional block cells of a given size, execute a quad-tree recursion on the two-dimensional density map structure in reduced Z-space to identify areas of different densities in the two dimensional matrix space, create an adaptive tile matrix representation of input matrix A, execute an adaptive tile matrix multiplication operation that performs dynamic tile-granular optimization based on density estimates and a cost mode, wherein the adaptive tile matrix multiplication operation utilizes multiple sockets of the multi-core computer processor executing in parallel, and transmit an indication of a result of said adaptive tile matrix multiplication operation to the real-time analytics, interactive data exploration and application platform.