A simple, yet powerful, learning method is presented by combining the famed kernel trick and the least-mean-square (LMS) algorithm, called the KLMS. General properties of the KLMS algorithm are demonstrated regarding its well-posedness in very high dimensional spaces using Tikhonov regularization theory. An experiment is studied to support our conclusion that the KLMS algorithm can be readily u...

An analytical solution is presented that reconstructs residual stress field from limited and incomplete data.  The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function.  This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon.  The analytical solu...

In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared with a non-cooperative agent which represents the average of the network. The analysis provides conditions under which diversity in the filter parameters is be...

Ensemble of networks has been proven to give better prediction result than a single network. Two commonly used way of determining the ensemble weights are simple average ensemble method and the generalized ensemble method. In the paper, we propose the weighted least square ensemble network. The major difference between this method and the other ensemble methods is that we do not assume that nei...

There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the optimization of discrete weak formulations, suitable finite element The main idea include neural-network function acting as control variable form. Finding that (quasi-) minimizes cost (or loss) functional, then yields approximation with desirable attr...

In this work, a new class of stochastic gradient algorithm is developed based on q-calculus. Unlike the existing q-LMS algorithm, the proposed approach fully utilizes the concept of q-calculus by incorporating time-varying q parameter. The proposed enhanced q-LMS (Eq-LMS) algorithm utilizes a novel, parameterless concept of error-correlation energy and normalization of signal to ensure high con...

In this paper, I develop an industry-level index of capital-embodied R&D by capturing the extent of research and development directed at the capital goods in which a given industry invests. Compiling and adjusting data from the National Science Foundation and Commerce Department, I construct industry-level, time-series measures of this index and investigate its properties. The data allow me to ...

This work is concerned with the development and study of a minimum residual norm subspace method based on the generalized conjugate residual method with inner orthogonalization (GCRO) method that allows flexible preconditioning and deflated restarting for the solution of nonsymmetric or non-Hermitian linear systems. First we recall the main features of flexible generalized minimum residual with...

one of the most valuable and important application of artificial satellites in geodetic sciences is recovery of the earth's gravity field. orbits of satellites either gravimetric or nongravimetric are analyzed to improve the earth's gravity field. gravimetric satellites are launched at low altitudes to observe gravity field in more detail. grace twin satellites are the second spacecra...