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Variational Methods of Approximation [PDF]
, 1976 In this chapter, we describe several of the more popular variational methods for the approximate solution of boundary-and initial-value problems. For ease in presentation, we confine our attention to linear problems, and most of what we present has to do with elliptic boundary-value problems. In particular, we discuss interpolation properties of finite
J. N. Reddy, J. T. Oden
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The Schwinger Variation Method
Journal of the Society for Industrial and Applied Mathematics, 1964Abstract : The Schwinger variation method is removed from its customary setting in Green's function theory, and is approached from the integral equations viewpoint. The traditional Schwinger theory is improved upon in two respects. Error bounds are provided for the approximations to A(f), a function determining waveguide transmission and reflection ...
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Variational transcorrelated method
The Journal of Chemical Physics, 2010We propose a new approach to the use of Jastrow ansatz in the calculation of electron correlations, based on a modification of the transcorrelated method of Boys and Handy [Proc. R. Soc. London, Ser. A 309, 209 (1969)]. In this new method, the original transcorrelated orbital equation is replaced with a general variational equation for the reference ...
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2000
Our final perturbation technique is the variational technique, which is particularly well-suited for finding approximations to ground-state energies and wave functions. We shall apply it, in particular, to find approximations to the ground-state energy and wave functions for the He atom.
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Our final perturbation technique is the variational technique, which is particularly well-suited for finding approximations to ground-state energies and wave functions. We shall apply it, in particular, to find approximations to the ground-state energy and wave functions for the He atom.
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1976
Publisher Summary There is an equivalence between problems in the calculus of variations and problems involving partial differential equations (PDE). In particular, any PDE problem can be phrased in variational form. The variational form permits a useful alternative approach to the solution of the PDE problem.
GEORGE F. CARRIER, CARL E. PEARSON
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Publisher Summary There is an equivalence between problems in the calculus of variations and problems involving partial differential equations (PDE). In particular, any PDE problem can be phrased in variational form. The variational form permits a useful alternative approach to the solution of the PDE problem.
GEORGE F. CARRIER, CARL E. PEARSON
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Variational method in a heterojunction
Physical Review B, 1991Determination des expressions analytiques de l'energie de l'etat fondamental et de la 1ere sous-bande d'une heterojonction en fonction de la temperature et de la concentration en electrons. La difference d'energie E 10 entre la premiere sous-bande et l'etat fondamental est en accord raisonnable avec les donnees obtenues dans une heterojonction GaAs-Ga
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Model-Based Clustering and Classification for Data Science, 2019
Bastian Goldluecke +8 more
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Bastian Goldluecke +8 more
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Six Variations on the Variational Method
1998As a graduate student in physics at the University of Michigan many years ago I had the good fortune to take a course in function theory from Norman Steenrod that pretty much changed the course of my life. My experience in that course plus several private conversations convinced me to switch out of physics and into mathematics.
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