Two numerical methods are presented for the periodic initial-value problem of the long wave–short wave interaction equations describing the interaction between one long longitudinal wave and two short transverse waves propagating in a generalized elastic medium. The first one is the relaxation method, which is implicit with second-order accuracy in both space and time. The second one is the spl...

The minimum `1-norm solution to an underdetermined system of linear equations y = Ax, is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signal processing and information transmission. However, general-purpose optimizers are much too slow for `1 minimization in many large-scale applications. The Homotopy method was originally propos...

The minimum `1-norm solution to an underdetermined system of linear equations y = Ax, is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signal processing and information transmission. However, general-purpose optimizers are much too slow for `1 minimization in many large-scale applications. The Homotopy method was originally propos...

The application of the fast gradient method to the dual QP leads to the Dual Fast Projected Gradient (DFPG) method. The DFPG converges with O ( k−2 ) rate, where k > 0 is the number of steps. At each step, it requires O(nm) operations. Therefore for a given ε > 0 an ε-approximation to the optimal dual function value

A two-step learning scheme for radial basis function neural networks, which combines the genetic algorithm (GA) with the hybrid learning algorithm (HLA), is proposed in this paper. It is compared with the methods of the GA, the recursive orthogonal least square algorithm (ROLSA) and another two-step learning scheme for RBF neural networks, which combines the K-means clustering with the HLA (K-m...

The feature based classification of remotely sensed image is used to assign corresponding levels with respect to groups with homogeneous characteristics, with the aim of discriminating multiple objects from each other within the image. Every level of an image is called class. This will be executed on the basis of spectral or spectrally defined features such as density, texture and many other th...

Neural networks are often used as a powerful discriminating estimator for tasks in system identification. This paper describes a neural-network-based method relies on the Radial Basis Function Network (RBF network), for estimating the variable damping factor C (n) and spring constant K (n) of a weighting platform. Firstly, the RBF network learns key properties of the step response of the weight...

In a recent article [2] Dutt, Greengard and Rohklin define two newmethods of deferred correction. Convergence for the the first method, using one step methods, has been proven in Hansen [8]. In this paper we augment the theory presented in [8] and use this to prove convergence for the second deferred correction method in [2] using linear k-step methods. This method has been known as Spectral De...