PARALLEL ALGORITHM FOR MULTI-DIMENSIONAL MATRIX MULTIPLICATION Research Paper

PARALLEL ALGORITHM FOR MULTI-DIMENSIONAL MATRIX MULTIPLICATION OPERATIONS REPRESENTATION USING KARNAUGH MAP - Research Paper Example The basic concept EKMR is to transform the multi-dimensional array in to a set of two-dimensional arrays. EKMR scheme implies Karnaugh Map which is a technique used to reduce a Boolean expression. It is commonly represented with the help of a rectangular map which holds all the possible values of the Boolean expression. Then the efficient data parallel algorithms for multi-dimensional matrix multiplication operation using EKMR are presented in this study which outperformed those data parallel algorithms for multi-dimensional matrix multiplication operation which used the TMR scheme. The study encourages designing data parallel algorithms for multi-dimensional dense and sparse multi-dimensional arrays for other operations as well using the EKMR scheme since this scheme produces the efficient performance for all dimensions and for all operations of the arrays. Multi-dimensional arrays which are also referred as tensors or n-ways arrays are usefully applied to a wide range of studies or methods such as climate modeling, finite element analysis (FEA), molecular dynamic and many more but still many issues have been encountered regarding efficient operations of these multi-dimensional arrays. Most of the proposed methods are successful in case of two-dimensional arrays which do not show accurate results when applied to the extended form of tensors. This occurred due to the traditional matrix representation (TMR) which is an array representation scheme that is commonly used to represent the multi-dimensional dense or sparse array. Dense and sparse are the two categories of the array form which are provided through the various data parallel programming languages [2] for instance, Vienna Fortran, High Performance Fortran, etc. If all or most of the array elements are non-zero values then it is called a dense array. On the other hand, if most of the elements of the array are zero then it is called a sparse array. When an operation is applied