Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation
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DOI：
10.1007/s13160-014-0156-2
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发表时间：
2014-10
影响因子：
0.9
通讯作者：
Kazuaki Tanaka;Akitoshi Takayasu;Xuefeng Liu;S. Oishi
中科院分区：
文献类型：
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作者：
Kazuaki Tanaka;Akitoshi Takayasu;Xuefeng Liu;S. Oishi
本文给出了线性椭圆算子可逆性的一种数值证明方法。该方法还提供了一个验证的范数估计的逆算子。这种类型的估计是重要的验证计算的解决方案，椭圆边值问题。所提出的方法使用广义特征值问题来获得范数估计。这种方法有几个优点。也就是说，它可以应用于两种类型的边界条件：Dirichlet型和Neumann型。它还提供了一种方法，数值计算的下限和上限的目标特征值。数值算例表明，该方法在大多数情况下提供了有效的估计。
This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimation is important for verified computations of solutions to elliptic boundary value problems. The proposed method uses a generalized eigenvalue problem to derive the norm estimation. This method has several advantages. Namely, it can be applied to two types of boundary conditions: the Dirichlet type and the Neumann type. It also provides a way of numerically evaluating lower and upper bounds of target eigenvalues. Numerical examples are presented to show that the proposed method provides effective estimations in most cases.