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変分法における直接解法 Direct method in the calculus of variations
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In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy. 数学の一トピックである変分法における直接解法(ちょくせつかいほう、英: direct method)とは、与えられた汎函数に対する最小点の存在の証明を構築するための一般的な手法である。1900年頃に、ザレンバとダフィット・ヒルベルトによって導入された。この手法は、函数解析学とトポロジーの手法に依拠するものである。解の存在を証明するために用いられるのと同様に、直接解法は解を所望の精度で計算するために用いられることもある。
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In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy. 数学の一トピックである変分法における直接解法(ちょくせつかいほう、英: direct method)とは、与えられた汎函数に対する最小点の存在の証明を構築するための一般的な手法である。1900年頃に、ザレンバとダフィット・ヒルベルトによって導入された。この手法は、函数解析学とトポロジーの手法に依拠するものである。解の存在を証明するために用いられるのと同様に、直接解法は解を所望の精度で計算するために用いられることもある。
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