Parallelize and Analysis Lu Factorization and Quadrant Interlocking Factorization Algorithm in Openmp

Abstract

Recent developments in high performance computer architecture have a significant effect on all fields of scientific computing. the solution of linear systems of equations lies at the heart of many applications in scientific computing. This paper describes, compare and analyzes the parallel LU factorization and QIF Factorization methods that are used in linear system solving on a multicore using OpenMP interface. In our work, illustrate that the QIF Algorithm performs better in performance compared to LU Factorization algorithm as it takes a small step to solve the problem.

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

“…Although some parts of the equation in LU factorization that consist many loops can be parallelized, the W Z factorization is uniquely known for its ability to offer parallelization. Even if W Z factorization and LU factorization are both implemented on OpenMP, the W Z factorization performs better in execution time than LU factorization when the number of thread increases [42,43].…”

Optimized Cramer’s Rule in WZ Factorization and Applications

“…LU factorization is often known to be implemented in LAPACK library to exploit the standard software library architectures [17]. W Z factorization offers parallelization in solving both sparse and dense linear system to enhance performance using OpenMP, CUDA, BLAS or EDK HW/SW codesign architecture [1,14]. Then, Yalamov [42] presented that W Z factorization is faster on computer with a parallel architecture than any other matrix factorization methods.…”