An introduction to functional analysis in computational mathematics
An introduction to functional analysis in computational mathematics
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计算数学泛函分析简介
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Viacheslav I. Lebedev
中科院分区：
文献类型：
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作者：
Viacheslav I. Lebedev
介绍泛函分析的基础知识，以及变分方程的元素(基于双线性形式)，包括Vishik-Lax-Milgram定理和椭圆型问题的广义解。在泛函分析方面，这样的计算数学问题被认为是各种逼近理论问题的极值--数值积分理论，二次泛函极小化的变分方法，以及求解算子方程的Galerkin和Ritz方法。此外，还介绍了迭代法的一般理论、切比申迭代法、合成法以及非线性分析的一些元素。还介绍了Sobolev空间和嵌入定理。
Presents the basics of functional analysis, as well as elements of variational equations (on the basis of bi-linear forms), including the Vishik-Lax-Milgram theorem and of generalized solutions of eliptic problems. In terms of functional analysis, such problems of computational mathematics are considered as extremal of problems of approximation theory of various types - the theory of numerical integration, variational methods of minimization of quadratic functional, and Galerkin and Ritz methods of finding solutions to operator equations. Also covered are: the general theory of iteration methods, Chebyshen iteration methods, composition method, along with some elements of nonlinear analysis. Sobolev spaces and embedding theorems are also introduced.