31501013
Preconditioning and convergence in the right norm
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.

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.
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.
7013408
Towards better making a decision in speaker verification
Speaker verification is a process that accepts or rejects the identity claim of a speaker. How to make a decision is a critical problem; a threshold for decision-making critically determines performance of a speaker verification system. Traditional threshold estimation methods take only information conveyed by training data into consideration and, to a great extent, do not relate it to production data. It turns out that a speaker verification system with such threshold estimation suffers from poor performance in reality due to mismatches. In this paper, we propose several methods towards better decision-making in a practical speaker verification system. Our methods include the use of additional reliable statistical information for threshold estimation, elimination of abnormal data for better estimation of underlying statistics, and on-line incremental threshold update. To evaluate the performance of our methods, we have done simulations based on a baseline system, Gaussian Mixture Model, in both text-dependent and text-independent modes. Comparative results show that in contrast to the recent threshold estimation methods our methods yield considerably better performance, especially on miscellaneous mismatch conditions, in terms of generalization. Thus our methods provide a promising way for real speaker verification applications.
16833900
Securely Sharing Data in Encrypted Databases
Collaborative design and application integration emphasize the demand for database security. Database encryption is widely adopted to ensure data privacy, which can prevent attacks from both outside intruders and inside malicious users. Current researches on this area are mainly focusing on encryption algorithms, key management and encryption efficiency. However, data sharing nature of database system is usually neglected. In this paper, we propose an access control model, 3S-RBAC, which enables data sharing while guaranteeing privacy. The model has many features: the novel concept of strong permission and weak permission; the hierarchy of database objects and keys; the permission and key inheritance; the binding of keys and permissions. Implementation in OSCAR Secure DBMS shows that the model is flexible, secure, practical, and can be integrated easily into existing enterprise applications
16708333
MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Time-Varying Lyapunov Equation Solving
This paper presents a new kind of recurrent neural network proposed by Zhang et al.for solving online Lyapunov equation with time-varying coefficient matrices. Global exponential convergence could be achieved by such a recurrent neural network when solving the time-varying problems in comparison with gradient neural networks (GNN). MATLAB simulation of both neural networks for the real-time solution of time-varying Lyapunov equation is then investigated through several important techniques. Computer-simulation results substantiate the theoretical analysis and demonstrate the efficacy of such a Zhang neural network (ZNN) on time-varying Lyapunov equation solving, especially when using power-sigmoid activation functions.
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.