论文标题
laplacian特征值的紧密外壳计算
Computation of Tight Enclosures for Laplacian Eigenvalues
论文作者
论文摘要
最近，对于组合用途的球形三角形，Laplace-Beltrami操作员的第一个特征值的高精度近似感兴趣。我们计算了这些特征值的改进和认证的外壳。这是通过以高精度应用特定溶液的方法来实现的，即通过间隔算术和泰勒模型的组合获得的外壳。特征值的索引通过利用相对于域的特征值的单调性来证明。通过将各个角落的膨胀和从内部的扩展相结合来处理经典的单一角落案例。特别是，这使我们能够为3D Kreweras模型计算100位基本特征值，这是先前努力的对象。
Recently, there has been interest in high-precision approximations of the first eigenvalue of the Laplace-Beltrami operator on spherical triangles for combinatorial purposes. We compute improved and certified enclosures to these eigenvalues. This is achieved by applying the method of particular solutions in high precision, the enclosure being obtained by a combination of interval arithmetic and Taylor models. The index of the eigenvalue is certified by exploiting the monotonicity of the eigenvalue with respect to the domain. The classically troublesome case of singular corners is handled by combining expansions at all corners and an expansion from an interior point. In particular, this allows us to compute 100 digits of the fundamental eigenvalue for the 3D Kreweras model that has been the object of previous efforts.
