186,665 research outputs found
On variations of power iteration
Abstract. The power iteration is a classical method for computing the eigenvector associated with the largest eigenvalue of a matrix. The subspace iteration is an extension of the power iteration where the subspace spanned by n largest eigenvectors of a matrix, is determined. The natural power iteration is an exemplary instance of the subspace iteration, providing a general framework for many principal subspace algorithms. In this paper we present variations of the natural power iteration, where n largest eigenvectors of a symmetric matrix without rotation ambiguity are determined, whereas the subspace iteration or the natural power iteration finds an invariant subspace (consisting of rotated eigenvectors). The resulting method is referred to as constrained natural power iteration and its fixed point analysis is given. Numerical experiments confirm the validity of our algorithm
High-precision elements of double-lined spectroscopic binaries from combined interferometry and spectroscopy. Application to the beta Cephei star beta Centauri
We present methodology to derive high-precision estimates of the fundamental
parameters of double-lined spectroscopic binaries. We apply the methods to the
case study of the double-lined beta Cephei star beta Centauri. We also present
a detailed analysis of beta Centauri's line-profile variations caused by its
oscillations. We point out that a systematic error in the orbital amplitudes,
and any quantities derived from them, occurs if the radial velocities of
blended component lines are computed without spectral disentangling. This
technique is an essential ingredient in the derivation of the physical
parameters if the goal is to obtain a precision of only a few percent. We have
devised iteration schemes to obtain the orbital elements for systems whose
lines are blended throughout the orbital cycle. We find the following
parameters for beta Cen: and , an age of years. We deduce two oscillation
frequencies for the broad-lined primary of beta Centauri with degrees higher
than 2. We propose that our iteration schemes be used in any future derivations
of the spectroscopic orbital parameters of double-lined binaries with blended
component lines to which disentangling can be successfully applied.Comment: 12 pages, 13 figures, accepted for publication in A&
Global design of analog cells using statistical optimization techniques
We present a methodology for automated sizing of analog cells using statistical optimization in a simulation based approach. This methodology enables us to design complex analog cells from scratch within reasonable CPU time. Three different specification types are covered: strong constraints on the electrical performance of the cells, weak constraints on this performance, and design objectives. A mathematical cost function is proposed and a bunch of heuristics is given to increase accuracy and reduce CPU time to minimize the cost function. A technique is also presented to yield designs with reduced variability in the performance parameters, under random variations of the transistor technological parameters. Several CMOS analog cells with complexity levels up to 48 transistors are designed for illustration. Measurements from fabricated prototypes demonstrate the suitability of the proposed methodology
Modeling and Energy Optimization of LDPC Decoder Circuits with Timing Violations
This paper proposes a "quasi-synchronous" design approach for signal
processing circuits, in which timing violations are permitted, but without the
need for a hardware compensation mechanism. The case of a low-density
parity-check (LDPC) decoder is studied, and a method for accurately modeling
the effect of timing violations at a high level of abstraction is presented.
The error-correction performance of code ensembles is then evaluated using
density evolution while taking into account the effect of timing faults.
Following this, several quasi-synchronous LDPC decoder circuits based on the
offset min-sum algorithm are optimized, providing a 23%-40% reduction in energy
consumption or energy-delay product, while achieving the same performance and
occupying the same area as conventional synchronous circuits.Comment: To appear in IEEE Transactions on Communication
On Resource Allocation in Fading Multiple Access Channels - An Efficient Approximate Projection Approach
We consider the problem of rate and power allocation in a multiple-access
channel. Our objective is to obtain rate and power allocation policies that
maximize a general concave utility function of average transmission rates on
the information theoretic capacity region of the multiple-access channel. Our
policies does not require queue-length information. We consider several
different scenarios. First, we address the utility maximization problem in a
nonfading channel to obtain the optimal operating rates, and present an
iterative gradient projection algorithm that uses approximate projection. By
exploiting the polymatroid structure of the capacity region, we show that the
approximate projection can be implemented in time polynomial in the number of
users. Second, we consider resource allocation in a fading channel. Optimal
rate and power allocation policies are presented for the case that power
control is possible and channel statistics are available. For the case that
transmission power is fixed and channel statistics are unknown, we propose a
greedy rate allocation policy and provide bounds on the performance difference
of this policy and the optimal policy in terms of channel variations and
structure of the utility function. We present numerical results that
demonstrate superior convergence rate performance for the greedy policy
compared to queue-length based policies. In order to reduce the computational
complexity of the greedy policy, we present approximate rate allocation
policies which track the greedy policy within a certain neighborhood that is
characterized in terms of the speed of fading.Comment: 32 pages, Submitted to IEEE Trans. on Information Theor
Convergence Analysis of Mixed Timescale Cross-Layer Stochastic Optimization
This paper considers a cross-layer optimization problem driven by
multi-timescale stochastic exogenous processes in wireless communication
networks. Due to the hierarchical information structure in a wireless network,
a mixed timescale stochastic iterative algorithm is proposed to track the
time-varying optimal solution of the cross-layer optimization problem, where
the variables are partitioned into short-term controls updated in a faster
timescale, and long-term controls updated in a slower timescale. We focus on
establishing a convergence analysis framework for such multi-timescale
algorithms, which is difficult due to the timescale separation of the algorithm
and the time-varying nature of the exogenous processes. To cope with this
challenge, we model the algorithm dynamics using stochastic differential
equations (SDEs) and show that the study of the algorithm convergence is
equivalent to the study of the stochastic stability of a virtual stochastic
dynamic system (VSDS). Leveraging the techniques of Lyapunov stability, we
derive a sufficient condition for the algorithm stability and a tracking error
bound in terms of the parameters of the multi-timescale exogenous processes.
Based on these results, an adaptive compensation algorithm is proposed to
enhance the tracking performance. Finally, we illustrate the framework by an
application example in wireless heterogeneous network
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