Electronic states on a fractal: Inverse-iteration method
نویسندگان
چکیده
منابع مشابه
INVERSE ITERATION FOR p-GROUND STATES
We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for p ∈ (1,∞) and a given domain Ω ⊂ Rn, we analyze a scheme that allows us to approximate the smallest value the ratio ∫ Ω |Dψ| pdx/ ∫ Ω |ψ| pdx can assume for functions ψ that vanish on ∂Ω. The scheme in question also provides a natural way to approximate minimizing ψ. Our an...
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Inverse iteration, if applied to a symmetric positive definite matrix, is shown to generate a sequence of iterates with monotonously decreasing Rayleigh quotients. We present sharp bounds from above and from below which highlight inverse iteration as a descent scheme for the Rayleigh quotient. Such estimates provide the background for the analysis of the behavior of the Rayleigh quotient in cer...
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Two-norm normalized inverse, shifted inverse, and Rayleigh quotient iteration are well-known algorithms for approximating an eigenvector of a symmetric matrix. In this work we establish rigorously that each one of these three algorithms can be viewed as a standard form of Newton’s method from the nonlinear programming literature, followed by the normalization. This equivalence adds considerable...
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Very often, inverse iteration is used with shifts to accelerate convergence to an eigenvector. In this paper, it is shown that, if the eigenvalue belongs to a nonlinear elementary divisor, the vector sequences may diverge even when the shift sequences converge to the eigenvalue. The local behavior is discussed through a 2 X 2 example, and a sufficient condition for the convergence of the vector...
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In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
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ژورنال
عنوان ژورنال: Physical Review B
سال: 1994
ISSN: 0163-1829,1095-3795
DOI: 10.1103/physrevb.49.14711