Research On Solving Method Of Sparse Linear Equations For Many-core Processors

Solving sparse linear equations is the core link of many scientific computing tasks and engineering problems.With the increase in the complexity of practical problems,it is particularly important to study the optimization of sparse linear equations.The existing method of summing partial values of variables optimizes the trigonometric solution.In the optimization,the dependencies between the variables are analyzed,and the partial correlation values of the variables are calculated by decomposing the sequence solving graph of the variables.Finally,all the partial values add up to get the final values of the variables.However,when the above method is directly used to solve the entire system of equations in the complete previous-generation process,it does not realize the optimization of the entire sparse linear equations.The reason is that the above method does not make full use of the partial values of the variables obtained in the previous generation of the solution,and the back-generation solution does not start until the previous-generation solution is completed.According to the shortcomings of the above method,this paper proposes a parallel solution algorithm of sparse linear equations based on the correlation decomposition method of the previous-generation-return variable solution.This algorithm makes full use of the middle of the previous-generation solution process when solving the entire sparse equations.Partial values are directly calculated to obtain the partial values of the variables related to the back-solving solution,and the partial values of the back-resolved variables can be calculated without waiting for all of the variables solved by the previous generation to be solved,effectively speeding up the solution of the equations.,To achieve the optimal solution of sparse linear equations.Aiming at solving the optimization problem of sparse linear equations,this paper proposes a parallel algorithm for solving sparse equations based on the correlation decomposition method of the previous-generation variable solution.The advantage of this algorithm is that the back generation solution can perform partial value calculation of the back generation solution without waiting for the completion of the previous generation solution,and does not need to analyze the complex structure of the sparse matrix in advance,which effectively saves the time of preprocessing and accelerates the solution of sparse linear equations.In the work of this paper,based on the experimental platform of many-core processors,the Florida sparse matrix is used to construct the sparse linear equations,and the parallel solution of the sparse linear equations based on the correlation decomposition method of the previous generation-back generation variable solution is realized,which verifies thefeasibility and efficiency of the proposed algorithm.The experimental results show that,compared with the cu SPARSE library function solving algorithm,the percentage of computational time reduction of the parallel algorithm proposed in this paper is more than 50%,and the maximum can be reduced by 99.6%,which significantly reduces the solution time of the sparse linear equations.The purpose of optimizing the sparse linear equations is solved.