Research On Matrix Computation Of GPU Acceleration

A lot of problems in high performance devote to research parallel algorithms implementation, matrix calculation is also a topic which is widely used in high-performance computing. With the development of technology and the increasing demand, serial algorithms have been unable to meet the needs of the study. Cluster can improve the performance partly, but low coupling of a cluster leds to its poor porbability,and it also leds to equipment cost and power consumption increase with calculation amount increacing. Graphics processor GPU(Graphic Process Unit) has powerful parallel processing capabilities, excellent floating-point calculation capabilities, high memory bandwidth, low cost, which is used to solve large-scale matrix computation.This paper studies three typical matrix topics: the approximation maximum eigenvalue of positive matrix, the approximation eigenvalue of general matrix and the inverse matrix of reversible matrix.Firstly, for the approximation maximum eigenvalue of positive matrix, the effective methods are all implemented with serial algorithms, so we implement the parallel algorithm(PA-ST: Parallel-Similarity Transformation) using the similarity transformation to solve the maximum eigenvalue of the positive matrix under CUDA,finally we achieved maximum speedup ratio of 30.028.Secondly, the most typical and effective parallel algorithm to solve the eigenvaluesof general matrix is QR algorithm, which is suitable for finding all eigenvalues. So we propoes the parallel approximation algorithm(PA: Pareallel-Approximate) to solve the approximation maximum eigenvalue of the general matrix under CUDA. The scope of the speedup ratio obtained is 15.424- 101.714.Finally, for the inverse matrix of reversible matrix, valid algorithms are currently serial programming ideas, with the increasing of the number of the matrix orders, theserial algorithms will be quite time-consuming undoubtedly. Thinking over the above presented problems, this paper proposes firstly GPU parallel Gauss-Jordan algorithm(PA-Gauss of Real Matrix) to solve the inverse matrix of real matrix and(PA-Gauss of Complex Matrix) to solve the inverse matrix of complex matrix. We obtain the maximum speedup ratio of 100 435 and 36508 respectively.We parallelize the core operations of algorithm, and do the CUDA optimization.Experiental results show that with the continuous increasing of the number of the matrix orders, the speedup is growing correspondingly, while the increasing in the number of iterations, the speedup ratio does not have clear change. So our algorithm is suitable for some larger number of iterations.