Error bounds in the Rayleigh-Ritz approximation of eigenvectors
نویسندگان
چکیده
منابع مشابه
Optimal a priori error bounds for the Rayleigh-Ritz method
We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.
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The investigation of symmetry nonrestoration scenarios has led to a controversy, with certain nonperturbative approximation schemes giving indications in sharp disagreement with those found within conventional perturbation theory. A Rayleigh-Ritz variational approach to the problem, which might be useful in bridging the gap between perturbative and nonperturbative viewpoints, is here proposed. ...
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We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics
سال: 1960
ISSN: 0022-4340
DOI: 10.6028/jres.064b.023