38388542
On a Class of Preconditioning Methods for Dense Linear Systems from Boundary Elements
In this paper we discuss several sparse-matrix-based preconditioners suitable for preconditioning dense linear systems of boundary element equations. All preconditioners involve only O(n) nonzeros. We provide a framework for constructing operator-splitting-based preconditioners and use it to analyze a class of sparse preconditioners. For singular integral equations, a more efficient preconditioner is proposed that has a band-2 structure.
21847139
An Analysis of Sparse Approximate Inverse Preconditioners for Boundary Integral Equations
Preconditioning techniques for dense linear systems arising from singular boundary integral equations are described and analyzed. A particular class of approximate inverse based preconditioners related to the mesh neighbor methods is known to be efficient. This paper shows that it is an operator splitting preconditioner and clusters eigenvalues for the normal equation matrix thus ensuring a fast convergence of the conjugate gradient normal method. Clustering of the eigenvalues of the preconditioned matrix and fast convergence of the generalized minimal residual method are also observed. For the type of problems considered, we demonstrate a crucial connection between two essential features of eigenvalue clustering for a sparse preconditioner---approximate inversion for a small cluster radius and operator splitting for a small cluster size. Experimental results from several boundary integral equations are presented.
25215706
On Two Variants of an Algebraic Wavelet Preconditioner
A recursive method of constructing preconditioning matrices for the nonsymmetric stiffness matrix in a wavelet basis is proposed for solving a class of integral and differential equations. It is based on a level-by-level application of the wavelet scales decoupling the different wavelet levels in a matrix form just as in the well-known nonstandard form. The result is a powerful iterative method with built-in preconditioning leading to two specific algebraic multilevel iteration algorithms: one with an exact Schur preconditioning and the other with an approximate Schur preconditioning. Numerical examples are presented to illustrate the efficiency of the new algorithms.
12726286
Fast Multilevel Algorithm for a Minimization Problem in Impulse Noise Removal
An effective 2-phase method for removing impulse noise was recently proposed. Its phase 1 identifies noisy pixel candidates by using median-type filters. Then in phase $2$, it restores only the noisy pixel candidates by some variational methods. The resulting method can handle salt-and-pepper noise and random-valued impulse noise at a level as high as 90% and 60%, respectively. The aim of this paper is to generalize a fast multilevel method for Gaussian denoising to solving the minimization problem arising in phase $2$ of the 2-phase method. The multilevel algorithm gives better images than standard optimization methods such as the Newton method or the conjugate gradient method. Also it can handle more general regularization functionals than the smooth ones previously considered. Supporting numerical experiments on two-dimensional gray-scale images are presented.
3879090
On A Recursive Schur Preconditioner For Iterative Solution Of A Class Of Dense Matrix Problems
There are currently several distinct preconditioning methods for dense matrices based on applying a wavelet transform to obtain a matrix with a large number of small entries. A sparse preconditioner for this transformed matrix can be formed by setting to zero entries that are assumed to be unimportant. The effectiveness of the preconditioner depends on retaining the most important entries and on ensuring that they are positioned conveniently within the transformed matrix. In this paper we present a new, recursive preconditioning strategy that takes into account more of the significant entries without greatly increasing cost and outperforms existing methods in certain cases.
15785287
A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration
Abstract
Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method (Chan et al., SIAM J. Sci. Comput. 20(6), 1964–1977, 1999) previously found reliable. Supporting numerical results are presented.

11647155
Methods of Combining Multiple Classifiers with Different Features and Their Applications to Text-Independent Speaker Identification
In practical applications of pattern recognition, there are often different features extracted from raw data which needs recognizing. Methods of combining multiple classifiers with different features are viewed as a general problem in various application areas of pattern recognition. In this paper, a systematic investigation has been made and possible solutions are classified into three frameworks, i.e. linear opinion pools, winner-take-all and evidential reasoning. For combining multiple classifiers with different features, a novel method is presented in the framework of linear opinion pools and a modified training algorithm for associative switch is also proposed in the framework of winner-take-all. In the framework of evidential reasoning, several typical methods are briefly reviewed for use. All aforementioned methods have already been applied to text-independent speaker identification. The simulations show that results yielded by the methods described in this paper are better than not only the individual classifiers' but also ones obtained by combining multiple classifiers with the same feature. It indicates that the use of combining multiple classifiers with different features is an effective way to attack the problem of text-independent speaker identification.
3106142
MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Online Solution of Linear Time-Varying Matrix Equation AXB-C=0
Different from gradient neural networks (GNN), a special kind ofrecurrent neural networks has been proposed recently by Zhanget alfor solving online linear matrix equations withtime-varying coefficients. Such recurrent neural networks, designedbased on a matrix-valued error-function, could achieve globalexponential convergence when solving online time-varying problemsin comparison with gradient neural networks. This paperinvestigates the MATLAB simulation of Zhang neural networks (ZNN)for real-time solution of linear time-varying matrix equationAXB- C= 0. Gradient neural networks aresimulated and compared as well. Simulation results substantiate thetheoretical analysis and efficacy of ZNN on linear time-varyingmatrix equation solving.
14996476
Global exponential convergence and stability of gradient-based neural network for online matrix inversion
Wang proposed a gradient-based neural network (GNN) to solve online matrix-inverses. Global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices. As compared to the previously-presented asymptotical convergence, this paper investigates more desirable properties of the gradient-based neural network; e.g., global exponential convergence for nonsingular matrix inversion, and global stability even for the singular-matrix case. Illustrative simulation results further demonstrate the theoretical analysis of gradient-based neural network for online matrix inversion.
1757195
Combining linear discriminant functions with neural networks for supervised learning
A novel supervised learning method is proposed by combining linear discriminant functions with neural networks. The proposed method results in a tree-structured hybrid architecture. Due to constructive learning, the binary tree hierarchical architecture is automatically generated by a controlled growing process for a specific supervised learning task. Unlike the classic decision tree, the linear discriminant functions are merely employed in the intermediate level of the tree for heuristically partitioning a large and complicated task into several smaller and simpler subtasks in the proposed method. These subtasks are dealt with by component neural networks at the leaves of the tree accordingly. For constructive learning, growing and credit-assignment algorithms are developed to serve for the hybrid architecture. The proposed architecture provides an efficient way to apply existing neural networks (e.g. multi-layered perceptron) for solving a large scale problem. We have already applied the proposed method to a universal approximation problem and several benchmark classification problems in order to evaluate its performance. Simulation results have shown that the proposed method yields better results and faster training in comparison with the multilayered perceptron.
640529
Heuristic Discovery of Role-Based Trust Chains in Peer-to-Peer Networks
Credential chains are needed in trusted peer-to-peer (P2P) applications, where trust delegation must be established between each pair of peers at specific role level. Role-based trust is refined from the coarse-grained trust model used in most P2P reputation systems. This paper offers a novel heuristic-weighting approach to selecting the most likely path to construct a role-based trust chain. We apply history-sensitive heuristics to measure the path complexity and assess the chaining efficiency. We discover successive edges of a trust chain, adaptively, to match with the demands from various P2P applications. New heuristic chaining algorithms are developed for backward, forward, and bi-directional discovery of trust chains. Our heuristic chain discovery scheme shortens the search time, reduces the memory requirement, and enhances the chaining accuracy in scalable P2P networks. Consider a trust graph over N credentials and M distinct role nodes. Our heuristic trust-chain discovery algorithms require O(N2 logN) search time and O(M) memory space, if the secondary heuristics are generated off-line in advance. These are improved from O(N3) search time and O(NM) space required in non-heuristic discovery algorithms by Li, Winsborough, and Mitchell (2003). Our analytical results are verified by extensive simulation experiments over typical classes of role-based trust graphs.