固有値問題の数理 : 近似解法から精度保証まで

概要

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An eigenvalue of an operator takes an important role to understand an nonlinear phenomenon in science and engineering. Especially, it often becomes a key value when we consider a behavior of dynamical systems. This article concerns with such an eigenvalue problem for matrices and differential operators. We first deal with a theoretical framework for it by introducing a concept of spectrum, and consider a matrix eigenvalue problem. Then we concern with an infinite dimensional eigenvalue problem, that is to obtain eigenvalues and eigenvectors for an operator in infinite dimensional domain of definition. We explain it from classical procedure to our recent results making use of the numerical verification methods. We also deal with some applications of the verified eigenvalues and eigenvectors to algebla, another numerical verification methods for nonlinear problems and stability analysis of bifurcation phenomenon in hydrodinamics.
2003-09-25