Nekrasov矩阵逆的无穷范数估计式的改进

Improvements on the estimation of infinity norm bound for the inverse of Nekrasov matrices

为了得到Nekrasov矩阵逆的无穷范数更为精确的估计式,通过引入带参数ε的正对角矩阵X,构造严格对角占优矩阵,并结合矩阵不等式的方法,给出了Nekrasov矩阵逆的无穷范数的新估计式。新估计式中含有确定范围的参数ε,因此,在实际应用中可以通过调节参数的值来得到更为精确的估计。然而,由于新估计式中含有参数ε,在理论上无法与已有结果进行直接比较。通过数值算例对新估计式与已有估计式进行了比较,结果表明,当选取适当参数ε时,新估计式比已有估计式的估计更精确。

In order to obtain a more accurate estimation of the infinity norm of the inverse of Nekrasov matrices,a new strictly diagonally dominant matrix is constructed by introducing a positive diagonal matrix X with parameter ε,and based on matrix inequality method,a new upper bound for the the infinity norm of the inverse of Nekrasov matrices is presented.The new bound contains a parameter ε which has a definite range of values;therefore,it can be used to get more accurate estimation by adjusting the value of the parameter in practice.However,because the new bound contains a parameter ε,it is impossible to compare directly with the existing estimations in theory.Therefore,a numerical example is given to compare the new bound with the existing estimations.The result shows that when the appropriate parameter ε is selected,the new bound is better than existing estimations.