Towards improved parallelism through order reduction of accessing data in nD matrices

This paper encompasses the presentation of an enhanced approach with the capacity to reduce the time complexity of accessing nodes in m-dimensional matrices from \(O(n^m)\) to \(O(n\log n)\) . The accomplishment of this process is attained by the serialization of nD (nD) matrices to single-dimensional arrays followed by the access of nodes accordingly. Linear representation of nD matrix data structure induces a superior parallelism of matrix calculations over dense, parallel core micro-architecture computers, including NVIDIA GPGPU Supercomputing and Intel Xeon Phi processing boards. This approach is feasibly implemented as the core of matrix data representation in Math software such as Matlab, Mathematica and Maple, in IDEs for more optimized code generation and in Parallel Computing Libraries such as CUBLAS and Magma.