论文标题
在参数自我辅助矩阵的光谱中定位锥形变性
Locating conical degeneracies in the spectra of parametric self-adjoint matrices
论文作者
论文摘要
提出了一个简单的迭代方案，用于定位2个参数的真实对称矩阵家族具有双重特征值的参数值。融合被证明是二次的。还描述了该方案的延伸到复杂的Hermitian矩阵（具有3个参数）和三重特征值的位置（实际对称矩阵的5个参数）。在几个例子中说明了算法融合：一个真实的对称家庭，一个复杂的遗传家庭，一个带有“避免过境”的矩阵家族（无覆盖）和一个5个参数的真实对称矩阵，带有三重特征值。
A simple iterative scheme is proposed for locating the parameter values for which a 2-parameter family of real symmetric matrices has a double eigenvalue. The convergence is proved to be quadratic. An extension of the scheme to complex Hermitian matrices (with 3 parameters) and to location of triple eigenvalues (5 parameters for real symmetric matrices) is also described. Algorithm convergence is illustrated in several examples: a real symmetric family, a complex Hermitian family, a family of matrices with an "avoided crossing" (no covergence) and a 5-parameter family of real symmetric matrices with a triple eigenvalue.
