Comparing Vectorization Techniques for Triangular Matrix Decomposition Computations

In this work we present a study on the vectorization of code segments that are typical for solving linear equation systems. We have selected Gaussian Elimination as representative of this type of problems. The sequential algorithm that performs this computation has a main loop with three nesting levels (indices i, j and k), that can be arranged according to six different organizations (called ijk forms). Out of these forms we chose the two most frequently used, which are, the kij form (or LU algorithm) and the jik form (or Crout algorithm) [2, 3]. 1 Introduction The Gaussian elimination of a N \Theta N matrix A is a standard problem of matrix algebra for reducing a matrix to upper triangular form U . The basica algorithm mimics the process of eliminating unknowns from the system of linear equations. As such it provides a direct method for solving linear equations. The matrix is premultiplied by a sequence of elementary lower triangular matrices, each chosen to introduce a column with ..