CAJ | 학술논문

为提高大型实对称矩阵数值求逆算法的运行速度，设计了一种分块迭代求逆算法，对算法做了详细的理论推导与分析。实现了四种常见的数值求逆算法，即Jacobi数值方法、QR分解法、LU分解法和高斯-约旦法，并分别与分块迭代求逆算法进行了对比分析。实验结果表明，在保证算法精度的情况下，分块迭代求逆算法极大的提高了算法的运行速度。当计算大小为700x700的实对称矩阵的逆矩阵时，相对于LU分解法，加速比为4倍；相对于QR分解法，加速比为26倍。
위제고대형실대칭구진수치구역산법적운행속도，설계료일충분괴질대구역산법，대산법주료상세적이론추도여분석。실현료사충상견적수치구역산법，즉Jacobi수치방법、QR분해법、LU분해법화고사-약단법，병분별여분괴질대구역산법진행료대비분석。실험결과표명，재보증산법정도적정황하，분괴질대구역산법겁대적제고료산법적운행속도。당계산대소위700x700적실대칭구진적역구진시，상대우LU분해법，가속비위4배；상대우QR분해법，가속비위26배。
In order to improve the running speed of the numerical inversion algorithm of real symmetric matrix, design a block iterative inversion algorithm to deduced and analysis the algorithm in detailed. And design four kinds of common numerical inversion algorithm, such as the Jacobi numerical method, QR decomposition method, LU decomposition method and Gauss Jordan method, compared with the block iterative inversion algorithm. The experimental results show that block iterative inversion algorithm improves the running speed of the algorithm greatly, while the precision maintains almost the same. When calculating the inverse matrix of the 700x700 matrix, the speedup is 4 times compared with the LU decomposition method, the speedup is 26 times compared with the QR decomposition method.