15,256 research outputs found
Convergence Analysis of Extended LOBPCG for Computing Extreme Eigenvalues
This paper is concerned with the convergence analysis of an extended
variation of the locally optimal preconditioned conjugate gradient method
(LOBPCG) for the extreme eigenvalue of a Hermitian matrix polynomial which
admits some extended form of Rayleigh quotient. This work is a generalization
of the analysis by Ovtchinnikov (SIAM J. Numer. Anal., 46(5):2567-2592, 2008).
As instances, the algorithms for definite matrix pairs and hyperbolic quadratic
matrix polynomials are shown to be globally convergent and to have an
asymptotically local convergence rate. Also, numerical examples are given to
illustrate the convergence.Comment: 21 pages, 2 figure
Quantization of Yang-Mills Theories without the Gribov Ambiguity
A gauge condition is presented here to quantize non-Abelian gauge theory on
the manifold , which is free from the
Gribov ambiguity. Perturbative calculations in the new gauge behave like the
axial gauge in ultraviolet region, while infrared behaviours of the
perturbative series are quite nontrivial. The new gauge condition, which reads
, may not satisfy the requirement that
in conventional perturbative calculations. However, such
contradiction is not harmful for gauge theories constructed on the manifold
.Comment: 11page
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