【摘要】 提出了厄米三对角矩阵本征问题的整体求解方法。它把本征值与对应的本征矢之间的内在联系用公式表示出来,使得在计算本征值时,几乎同时求出了本征矢。采用本文提出的选取分界点的方法,可以使本征失的计算精度与本征值的精度具有相同数量级。这一方法可以用来处理维数十分大的体系。更多还原

【Abstract】 An integrated method for solving the eigenvalue problem of a hermitiantridiagonal matrix is presented. In this method, an intrinsic relation between theeigenvalue and its corresponding eigenvector is formulated so that the calculationof the eigenvector is accompli shed almost simultaneously with the determinationof the eigenvalue. With the proper choice of pivoting, it is shown that theaccuracy of the calculated eigenvector can be made to be of the same order ofmagnitude as that of the eigenvalue. The method can readily be used to handlematrices of unusually large sizes.更多还原