30,178 research outputs found
Efficient Recursion Method for Inverting Overlap Matrix
A new O(N) algorithm based on a recursion method, in which the computational
effort is proportional to the number of atoms N, is presented for calculating
the inverse of an overlap matrix which is needed in electronic structure
calculations with the the non-orthogonal localized basis set. This efficient
inverting method can be incorporated in several O(N) methods for
diagonalization of a generalized secular equation. By studying convergence
properties of the 1-norm of an error matrix for diamond and fcc Al, this method
is compared to three other O(N) methods (the divide method, Taylor expansion
method, and Hotelling's method) with regard to computational accuracy and
efficiency within the density functional theory. The test calculations show
that the new method is about one-hundred times faster than the divide method in
computational time to achieve the same convergence for both diamond and fcc Al,
while the Taylor expansion method and Hotelling's method suffer from numerical
instabilities in most cases.Comment: 17 pages and 4 figure
Ignorance and indifference
The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the 'principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. Copyright 2008 by the Philosophy of Science Association. All rights reserved
An alternative approach to KP hierarchy in matrix models
We show that there exists an alternative procedure in order to extract
differential hierarchies, such as the KdV hierarchy, from one--matrix models,
without taking a continuum limit. To prove this we introduce the Toda lattice
and reformulate it in operator form. We then consider the reduction to the
systems appropriate for one--matrix model.Comment: 18
Domain decomposition improvement of quark propagator estimation
Applying domain decomposition to the lattice Dirac operator and the
associated quark propagator, we arrive at expressions which, with the proper
insertion of random sources therein, can provide improvement to the estimation
of the propagator. Schemes are presented for both open and closed (or loop)
propagators. In the end, our technique for improving open contributions is
similar to the ``maximal variance reduction'' approach of Michael and Peisa,
but contains the advantage, especially for improved actions, of dealing
directly with the Dirac operator. Using these improved open propagators for the
Chirally Improved operator, we present preliminary results for the static-light
meson spectrum. The improvement of closed propagators is modest: on some
configurations there are signs of significant noise reduction of disconnected
correlators; on others, the improvement amounts to a smoothening of the same
correlators.Comment: 19 pages, 8 figures, version to appear in Computer Physics
Communication
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