Improved conjugate gradient implementation for least squares support vector machines

As a promising method for pattern recognition and function estimation, least squares support vector machines (LS-SVM) express the training in terms of solving a linear system instead of a quadratic programming problem as for conventional support vector machines (SVM). In this paper, by using the information provided by the equality constraint, we transform the minimization problem with a single equality constraint in LS-SVM into an unconstrained minimization problem, then propose reduced formulations for LS-SVM. By introducing this transformation, the times of using conjugate gradient (CG) method, which is a greatly time-consuming step in obtaining the numerical solution, are reduced to one instead of two as proposed by Suykens et al. (1999). The comparison on computational speed of our method with the CG method proposed by Suykens et al. and the first order and second order SMO methods on several benchmark data sets shows a reduction of training time by up to 44%. (C) 2011 Elsevier B.V. All rights reserved.

Semi batch learning with store management using enhanced conjugate gradient

This paper explores the performance of sliding-window based training, termed as semi batch, using multilayer perceptron (MLP) neural network in the presence of correlated data. The sliding window training is a form of higher order instantaneous learning strategy without the need of covariance matrix, usually employed for modeling and tracking purposes. Sliding-window framework is implemented to combine the robustness of offline learning algorithms with the ability to track online the underlying process of a function. This paper adopted sliding window training with recent advances in conjugate gradient direction with application of data store management e.g. simple distance measure, angle evaluation and the novel prediction error test. The simulation results show the best convergence performance is gained by using store management techniques. © 2012 Springer-Verlag.

Evaluating Asymmetric Multicore Systems-on-Chip using Iso-Metrics

The end of Dennard scaling has pushed power consumption into a first order concern for current systems, on par with performance. As a result, near-threshold voltage computing (NTVC) has been proposed as a potential means to tackle the limited cooling capacity of CMOS technology. Hardware operating in NTV consumes significantly less power, at the cost of lower frequency, and thus reduced performance, as well as increased error rates. In this paper, we investigate if a low-power systems-on-chip, consisting of ARM's asymmetric big.LITTLE technology, can be an alternative to conventional high performance multicore processors in terms of power/energy in an unreliable scenario. For our study, we use the Conjugate Gradient solver, an algorithm representative of the computations performed by a large range of scientific and engineering codes.

R-matrix-Floquet theory of multiphoton processes:VIII. A linear equations method

A new linear equations method for calculating the R-matrix, which arises in the R-matrix-Floquet theory of multiphoton processes, is introduced. This method replaces the diagonalization of the Floquet Hamiltonian matrix by the solution of a set of linear simultaneous equations which are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readily ported onto parallel computers. It will thus enable much larger problems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are important. Finally, an alternative linear equations method, which avoids the explicit calculation of the R-matrix by incorporating the boundary conditions directly, is described in an appendix.

Performance and Fault Tolerance of Preconditioned Iterative Solvers on Low-Power ARM Architectures

As the complexity of computing systems grows, reliability and energy are two crucial challenges asking for holistic solutions. In this paper, we investigate the interplay among concurrency, power dissipation, energy consumption and voltage-frequency scaling for a key numerical kernel for the solution of sparse linear systems. Concretely, we leverage a task-parallel implementation of the Conjugate Gradient method, equipped with an state-of-the-art pre-conditioner embedded in the ILUPACK software, and target a low-power multi core processor from ARM.In addition, we perform a theoretical analysis on the impact of a technique like Near Threshold Voltage Computing (NTVC) from the points of view of increased hardware concurrency and error rate.

The Galactic metallicity gradient

We have previously published intermediate to hi,oh resolution spectroscopic observations of approximately 80 early B-type main-sequence stars situated in 19 Galactic open clusters/associations with Galactocentric distances distributed over 6 less than or equal to R-g less than or equal to 18 kpc. This current study collates and re-analyses these equivalent- width datasets using LTE and non-LTE model atmosphere techniques, in order to determine the stellar atmospheric parameters and abundance estimates for C, N, O, Mg, Al and Si. The latter should be representative of the present-day Galactic interstellar medium. Our extensive observational dataset permits the identification of sub-samples of stars with similar atmospheric parameters and of homogeneous subsets of lines. As such, this investigation represents the most extensive and systematic study of its kind to date. We conclude that the distribution of light elements (CI O, Mg & Si) in the Galactic disk can be represented by a linear, radial gradient of -0.07 +/- 0.01 dex kpc(-1) Our results for nitrogen and oxygen viz. (-0.09 +/- 0.01 dex kpc(-1) and -0.067 +/- 0.008 dex kpc(-1)) are in excellent agreement with that found from the study of HII regions. We have also examined our datasets for evidence of an abrupt discontinuity in the metallicity of the Galactic disk near a Galactocentric distance of 10 kpc (see Twarog et al. 1997). However, there is no evidence to suggest that our data would be better fitted with a two-zone model. Moreover, we observe a N/O gradient of -0.04 +/- 0.02 dex kpc(-1) which is consistent with that found for other spiral galaxies (Vila- Costas gr Edmunds 1993).

One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

tts: A SAT-Solver for Small, Difficult Instances

The Ternary Tree Solver (tts) is a complete solver for propositional satisfiability which was designed to have good performance on the most difficult small instances. It uses a static ternary tree data structure to represent the simplified proposition under all permissible partial assignments and maintains a database of derived propositions known to be unsatisfiable. In the SAT2007 competition version 4.0 won the silver medal for the category handmade, speciality UNSAT solvers and was the top qualifier for the second stage for handmade benchmarks, solving 11 benchmarks which were not solved by any other entrant. We describe the methods used by the solver and analyse the competition Phase 1 results on small benchmarks. We propose a first version of a comprehensive suite of small difficult satisfiability benchmarks (sdsb) and compare the worst-case performance of the competition medallists on these benchmarks.