求解Toeplitz矩阵特征值反问题的不精确牛顿方法

The inexact Newton method for inverse Toeplitz eigenvalue problems

研究了求解大型Toeplitz矩阵特征值反问题的数值方法。用迭代方法(内迭代)求这些线性方程组的近似解,给出了求解大型Toeplitz矩阵特征值反问题的不精确牛顿方法。该方法可避免牛顿方法的"过度求解问题",改进牛顿方法的有效性。数值结果表明不精确牛顿方法优于牛顿方法。

Numerical methods for solving large inverse Toeplitz eigenvalue problems were studied. The inexact Newton method for solving large inverse Toeplitz eigenvalue problem was given by using iterative methods（ inner iterations） for solving these systems approximately. This method call avoid the oversolving problems of Newton methods and hence improve the efficiency. The numerical results show that the inexact Newton method is better than the Newton method.