Parallel Triangular Matrix Inversion With Increased Parallelism And Less Use of Shared Memory

A triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Conversely a square matrix is called upper triangular if all the entries below the main diagonal are zero. [6] For a square matrix M , M−1 is the inverse matrix where M ×M−1 = I and I denotes the n× n identity matrix. We say that the problem size of computing the inversion of a triangular Matrix M with dimension n, is n. Matrix inversion has innately some sequential steps, and the size of the problem at each step is remarkably large comaring to the size of the original problem. Many approaches have been proposed to either reduce the size of the sequential parts, increase concurrency [2] or use the memory efficiently[1]. In this project, a parallel algorithm for computing inversion of a triangular is proposed, and implemented in OpenMP. This algorithm relies on extended concurrency and efficient processor communication.