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2010
The saddle point method is an asymptotic method to calculate integrals of the type $$ \int_{-\infty}^{\infty} e^{n\phi(x)} dx $$ (32.1) for large n. If the function o(x) has a maximum at x 0 , then the integrand also has a maximum there which becomes very sharp for large n.
Sighart F. Fischer +1 more
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The saddle point method is an asymptotic method to calculate integrals of the type $$ \int_{-\infty}^{\infty} e^{n\phi(x)} dx $$ (32.1) for large n. If the function o(x) has a maximum at x 0 , then the integrand also has a maximum there which becomes very sharp for large n.
Sighart F. Fischer +1 more
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Must saddle point electrons always ride on the saddle? [PDF]
Journal of Physics B: Atomic, Molecular and Optical Physics, 2002 The transfer ionization of He and H2 by incident He2+ was investigated at 0.81 au impact velocity employing cold target recoil ion momentum spectroscopy. In addition to electrons in the saddle point region between the target and projectile forming two `jets' separated by a valley along the projectile beam axis, we find a new group of electrons ...
Reinhard Dörner +6 more
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1970
The classical instances of saddle point theorems are the minimax theorems of v. Neumann [1] (6.1.1) and Kakutani [3]. Since then the saddle point concept has been found to apply in a much larger context. It is also a natural and rich source for duality theorems.
Josef Stoer, Christoph Witzgall
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The classical instances of saddle point theorems are the minimax theorems of v. Neumann [1] (6.1.1) and Kakutani [3]. Since then the saddle point concept has been found to apply in a much larger context. It is also a natural and rich source for duality theorems.
Josef Stoer, Christoph Witzgall
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On Convergence of the Arrow–Hurwicz Method for Saddle Point Problems
Journal of Mathematical Imaging and Vision, 2022B. He, Sheng Xu, Xiaoming Yuan
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1980
Publisher Summary This chapter presents a simple critical point theorem for certain indefinite functionals. The result follows from a theorem by Ekeland on the minimization of non-convex functionals and provides a generalization of a recent minimax theorem due to Lazer, Landesman, and Meyers. The advantages of the Ekeland theorem over the main result
Peter W. Bates, Ivar Ekeland
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Publisher Summary This chapter presents a simple critical point theorem for certain indefinite functionals. The result follows from a theorem by Ekeland on the minimization of non-convex functionals and provides a generalization of a recent minimax theorem due to Lazer, Landesman, and Meyers. The advantages of the Ekeland theorem over the main result
Peter W. Bates, Ivar Ekeland
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Computation of saddle point of attachment
22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1991Low-speed flows over a cylinder mounted on a flat plate are studied numerically in order to confirm the existence of a saddle point of attachment in the flow before an obstacle, to analyze the flow characteristics near the saddle point theoretically, and to address the significance of the saddle point of attachment to the construction of external flow ...
Chao Ho Sung +2 more
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2016
Standard numerical methods fail to provide accurate approximations when partial differential equations involve constraints defined by a differential operator or when they contain terms weighted by a larger parameter. Generalizations of the Lax–Milgram and Cea lemmas provide a concise framework for the development and analysis of appropriate numerical ...
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Standard numerical methods fail to provide accurate approximations when partial differential equations involve constraints defined by a differential operator or when they contain terms weighted by a larger parameter. Generalizations of the Lax–Milgram and Cea lemmas provide a concise framework for the development and analysis of appropriate numerical ...
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Nonlinear Analysis: Theory, Methods & Applications, 2005
From the beginning of the calculus of variations over 300 years ago, scientists were interested in finding extrema of expressions (now called functionals) involving unknown functions. It was discovered that functions producing extrema are solutions of differential equations (called Euler equations).
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From the beginning of the calculus of variations over 300 years ago, scientists were interested in finding extrema of expressions (now called functionals) involving unknown functions. It was discovered that functions producing extrema are solutions of differential equations (called Euler equations).
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1971
In this section, we consider the linear system $${\rm{\dot u}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{u}}_{\rm{t}} } \right)$$ (26.1) and the perturbed linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{x}}_{\rm{t}} } \right) + {\rm{f}}\left( {{\rm{x}}_{\rm{t}} } \right)$$ (26.2) where $${\rm{L ...
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In this section, we consider the linear system $${\rm{\dot u}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{u}}_{\rm{t}} } \right)$$ (26.1) and the perturbed linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{x}}_{\rm{t}} } \right) + {\rm{f}}\left( {{\rm{x}}_{\rm{t}} } \right)$$ (26.2) where $${\rm{L ...
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The Arabian journal for science and engineering, 2021
K. Gangadhar +3 more
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K. Gangadhar +3 more
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