On the use of direct variational methods in applicationsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:At present, the calculus of variations is an area of great importance in modern mathematics. The variational approach is needed in topology, functional analysis, and computational mathematics for solving problems in physics, mechanics, and economics. Another reason for increased interest in direct methods is that high-performance computers and, accordingly, efficient numerical methods are now available. In the theory of ill-posed inverse problems, the variational approach is usually used to find solutions. It is necessary to develop a universal method for solving ill-posed problems basing on A.N. Tikhonov's ideas and theorems.