求解病态线性方程组的预处理精细积分法
摘要
In order to reduce the condition number of the coefficient matrix of ill-conditioned linear equations, according to the equilibration thought for matrices, a 1-norm equilibration method was proposed to properly reduce the condition number of the matrix, and expanded to the norm equilibration methods. Then, the norm equilibration method together with the precise integration method was combined for solving ill-conditioned linear equations. The numerical results confirm that, the accuracy, efficiency and application scope of the preconditioned precise integration method for ill-conditioned linear equations all improve significantly (the number of significant digits increases by more than 5 and the number of iterations decreases by about 15). In these methods, the preconditioned precise integration method of 1-norm equilibration is the best.