论文标题
关于反向Sturm-Liouville问题的复杂性
On the complexity of the inverse Sturm-Liouville problem
论文作者
论文摘要
本文探讨了与罗宾边界条件解决逆sturm-liouville问题相关的复杂性：给定一系列特征值和一系列规范常数，通用算法需要多少限制才能返回潜力和边界条件？结果表明，如果几乎有限的许多特征值和规范常数与零电势相一致，那么限制的数量为零，即可以在许多步骤中以有限的许多步骤来检索电势和边界条件。否则，结果表明此问题需要一个限制。此外，如果一个人对特征值和规范常数与零电势问题的差异有多大控制，并且知道电势的平均值为零，则可以通过完全误差控制执行计算。这是本着解决性复杂性指数的精神进行的。所有算法都与数值示例一起明确提供。
This paper explores the complexity associated with solving the inverse Sturm-Liouville problem with Robin boundary conditions: given a sequence of eigenvalues and a sequence of norming constants, how many limits does a universal algorithm require to return the potential and boundary conditions? It is shown that if all but finitely many of the eigenvalues and norming constants coincide with those for the zero potential then the number of limits is zero, i.e. it is possible to retrieve the potential and boundary conditions precisely in finitely many steps. Otherwise, it is shown that this problem requires a single limit; moreover, if one has a priori control over how much the eigenvalues and norming constants differ from those of the zero-potential problem, and one knows that the average of the potential is zero, then the computation can be performed with complete error control. This is done in the spirit of the Solvability Complexity Index. All algorithms are provided explicitly along with numerical examples.
