A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Long Wavelength Peristaltic Transport of Non-Newton Fluids

Solutions are obtained for the stream function and the pressure field for the flow of non-Newtonian fluids in a tube by long peristaltic waves of arbitrary shape. The axial velocity profiles and stress distributions on the wall are discussed for particular waves of some practical interest. The effect of non- Newtonian character of the fluid is examined.

Sustaining productivity of a Vertosol at Warra, Queensland, with fertilisers, no-tillage or legumes. 8. Effect of duration of lucerne ley on soil nitrogen and water, wheat yield and protein.

Soil nitrogen (N) supply in the Vertosols of southern Queensland, Australia has steadily declined as a result of long-term cereal cropping without N fertiliser application or rotations with legumes. Nitrogen-fixing legumes such as lucerne may enhance soil N supply and therefore could be used in lucerne-wheat rotations. However, lucerne leys in this subtropical environment can create a soil moisture deficit, which may persist for a number of seasons. Therefore, we evaluated the effect of varying the duration of a lucerne ley (for up to 4 years) on soil N increase, N supply to wheat, soil water changes, wheat yields and wheat protein on a fertility-depleted Vertosol in a field experiment between 1989 and 1996 at Warra (26degrees 47'S, 150degrees53'E), southern Queensland. The experiment consisted of a wheat-wheat rotation, and 8 treatments of lucerne leys starting in 1989 (phase 1) or 1990 (phase 2) for 1,2,3 or 4 years duration, followed by wheat cropping. Lucerne DM yield and N yield increased with increasing duration of lucerne leys. Soil N increased over time following 2 years of lucerne but there was no further significant increase after 3 or 4 years of lucerne ley. Soil nitrate concentrations increased significantly with all lucerne leys and moved progressively downward in the soil profile from 1992 to 1995. Soil water, especially at 0.9-1.2 m depth, remained significantly lower for the next 3 years after the termination of the 4 year lucerne ley than under continuous wheat. No significant increase in wheat yields was observed from 1992 to 1995, irrespective of the lucerne ley. However, wheat grain protein concentrations were significantly higher under lucerne-wheat than under wheat wheat rotations for 3-5 years. The lucerne yield and soil water and nitrate-N concentrations were satisfactorily simulated with the APSIM model. Although significant N accretion occurred in the soil following lucerne leys, in drier seasons, recharge of the drier soil profile following long duration lucerne occurred after 3 years. Consequently, 3- and 4-year lucerne-wheat rotations resulted in more variable wheat yields than wheat-wheat rotations in this region. The remaining challenge in using lucerne-wheat rotations is balancing the N accretion benefits with plant-available water deficits, which are most likely to occur in the highly variable rainfall conditions of this region.

Poor adoption of ley-pastures in south-west Queensland: biophysical, economic and social constraints.

The present review identifies various constraints relating to poor adoption of ley-pastures in south-west Queensland, and suggests changes in research, development and extension efforts for improved adoption. The constraints include biophysical, economic and social constraints. In terms of biophysical constraints, first, shallower soil profiles with subsoil constraints (salt and sodicity), unpredictable rainfall, drier conditions with higher soil temperature and evaporative demand in summer, and frost and subzero temperature in winter, frequently result in a failure of established, or establishing, pastures. Second, there are limited options for legumes in a ley-pasture, with the legumes currently being mostly winter-active legumes such as lucerne and medics. Winter-active legumes are ineffective in improving soil conditions in a region with summer-dominant rainfall. Third, most grain growers are reluctant to include grasses in their ley-pasture mix, which can be uneconomical for various reasons, including nitrogen immobilisation, carryover of cereal diseases and depressed yields of the following cereal crops. Fourth, a severe depletion of soil water following perennial ley-pastures (grass + legumes or lucerne) can reduce the yields of subsequent crops for several seasons, and the practice of longer fallows to increase soil water storage may be uneconomical and damaging to the environment. Economic assessments of integrating medium- to long-term ley-pastures into cropping regions are generally less attractive because of reduced capital flow, increased capital investment, economic loss associated with establishment and termination phases of ley-pastures, and lost opportunities for cropping in a favourable season. Income from livestock on ley-pastures and soil productivity gains to subsequent crops in rotation may not be comparable to cropping when grain prices are high. However, the economic benefits of ley-pastures may be underestimated, because of unaccounted environmental benefits such as enhanced water use, and reduced soil erosion from summer-dominant rainfall, and therefore, this requires further investigation. In terms of social constraints, the risk of poor and unreliable establishment and persistence, uncertainties in economic and environmental benefits, the complicated process of changing from crop to ley-pastures and vice versa, and the additional labour and management requirements of livestock, present growers socially unattractive and complex decision-making processes for considering adoption of an existing medium- to long-term ley-pasture technology. It is essential that research, development and extension efforts should consider that new ley-pasture options, such as incorporation of a short-term summer forage legume, need to be less risky in establishment, productive in a region with prevailing biophysical constraints, economically viable, less complex and highly flexible in the change-over processes, and socially attractive to growers for adoption in south-west Queensland.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

A fast quasi-Newton method for semi-supervised SVM

Due to its wide applicability, semi-supervised learning is an attractive method for using unlabeled data in classification. In this work, we present a semi-supervised support vector classifier that is designed using quasi-Newton method for nonsmooth convex functions. The proposed algorithm is suitable in dealing with very large number of examples and features. Numerical experiments on various benchmark datasets showed that the proposed algorithm is fast and gives improved generalization performance over the existing methods. Further, a non-linear semi-supervised SVM has been proposed based on a multiple label switching scheme. This non-linear semi-supervised SVM is found to converge faster and it is found to improve generalization performance on several benchmark datasets. (C) 2010 Elsevier Ltd. All rights reserved.

Modified Newton, rank-1 Broyden update and rank-2 BFGS update methods in helicopter trim: A comparative study

Nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For strongly nonlinear problems, the solution obtained in the iterative process can diverge due to numerical instability. As a result, the application of numerical simulation for strongly nonlinear problems is limited. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. Reliable solution methods which do not need Jacobian calculation at each iteration are needed for this problem. In this paper, a comparative study is done by incorporating different methods for solving the nonlinear equations in helicopter trim. Three different methods based on calculating the Jacobian at the initial guess are investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Smoothed functional and Quasi-Newton algorithms for routing in multi-stage queueing network with constraints

We consider the problem of optimal routing in a multi-stage network of queues with constraints on queue lengths. We develop three algorithms for probabilistic routing for this problem using only the total end-to-end delays. These algorithms use the smoothed functional (SF) approach to optimize the routing probabilities. In our model all the queues are assumed to have constraints on the average queue length. We also propose a novel quasi-Newton based SF algorithm. Policies like Join Shortest Queue or Least Work Left work only for unconstrained routing. Besides assuming knowledge of the queue length at all the queues. If the only information available is the expected end-to-end delay as with our case such policies cannot be used. We also give simulation results showing the performance of the SF algorithms for this problem.

A Vision-Based Micro-Newton Static Force Sensor Using a Displacement-Amplifying Compliant Mechanism (DaCM)

A micro-newton static force sensor is presented here as a packaged product. The sensor, which is based on the mechanics of deformable objects, consists of a compliant mechanism that amplifies the displacement caused by the force that is to be measured. The output displacement, captured using a digital microscope and analyzed using image processing techniques, is used to calculate the force using precalibrated force-displacement curve. Images are scanned in real time at a frequency of 15 frames per second and sampled at around half the scanning frequency. The sensor was built, packaged, calibrated, and tested. It has simulated and measured stiffness values of 2.60N/m and 2.57N/m, respectively. The smallest force it can reliably measure in the presence of noise is about 2 mu N over a range of 1.4mN. The off-the-shelf digital microscope aside, all of its other components are purely mechanical; they are inexpensive and can be easily made using simple machines. Another highlight of the sensor is that its movable and delicate components are easily replaceable. The sensor can be used in aqueous environment as it does not use electric, magnetic, thermal, or any other fields. Currently, it can only measure static forces or forces that vary at less than 1Hz because its response time and bandwidth are limited by the speed of imaging with a camera. With a universal serial bus (USB) connection of its digital microscope, custom-developed graphical user interface (GUI), and related software, the sensor is fully developed as a readily usable product.

Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar, Dukkipati, & Bhatnagar, 2014), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on SF algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms. (C) 2014 Elsevier Ltd. All rights reserved.