12795975
Tikhonov regularization for weighted total least squares problems
In this work, we study and analyze the regularized weighted total least squares (RWTLS) formulation. Our regularization of the weighted total least squares problem is based on the Tikhonov regularization. Numerical examples are presented to demonstrate the effectiveness of the RWTLS method.
7039845
An Algorithm for Solving Scaled Total Least Squares Problems
In this paper, we present a rankrevealing two-sided orthogonal decomposition method for solving the STLS problem. An error analysis of the algorithm is given. Our numerical experiments show that this algorithm computes the STLS solution as accurate as the SVD method with less computation.
21408324
A Stability Property of T. Chan's Preconditioner
In this short note, we prove that T. Chan's preconditioner proposed in {TChan} [SIAM J. Sci. Statist. Comput., 9 (1988), pp. 766--771] is stable for matrices that are normal and stable.
9180515
Incremental Spectral Clustering With Application to Monitoring of Evolving Blog Communities
In recent years, spectral clustering method has gained attentions because of its superior performance compared to other traditional clustering algorithms such as K-means algorithm. The existing spectral clustering algorithms are all off-line algorithms, i.e., they can not incrementally update the clustering result given a small change of the data set. However, the capability of incrementally updating is essential to some applications such as real time monitoring of the evolving communities of websphere or blogsphere. Unlike traditional stream data, these applications require incremental algorithms to handle not only insertion/deletion of data points but also similarity changes between existing items. This paper extends the standard spectral clustering to such evolving data by introducing the incidence vector/matrix to represent two kinds of dynamics in the same framework and by incrementally updating the eigenvalue system. Our incremental algorithm, initialized by a standard spectral clustering, continuously and efficiently updates the eigenvalue system and generates instant cluster labels, as the data set is evolving. The algorithm is applied to a blog data set. Compared with recomputation of the solution by standard spectral clustering, it achieves similar accuracy but with much lower computational cost. Close inspection into the blog content shows that the incremental approach can discover not only the stable blog communities but also the evolution of the individual multi-topic blogs.
13976369
Design of a nanosensor array architecture
This paper describes a nanowire sensor array architecture for high-speed, high-accuracy sensor systems. The chip has very simple processing elements (PEs) in a massively parallel architecture, in which each PE is directly connected to seven sensors. A sampling rate of 100 ns is enough to realized high-speed sensing feedback for electronic nose. We aim to create a very simple architecture, because a compact design is required ton integrate as many PEs as possible on a single chip. A widely used, easy to implement estimator-minimum distance classifier is introduced to realize the pattern recognition. A sample design is implemented in VHDL and has been simulated and synthesized using TSMC 0.25 standard cell library and a commercial 0.16 standard cell library.
115232895
Elastostatic inverse formulation
Abstract. In this paper an inverse method for solving elastostatic problems with incomplete boundary conditions is presented. In general, inverse problems are ill-posed boundary value problems whose stability and uniqueness of solution and sensitivity-based formulations require additional constraints. In the development we use the Betti-reciprocal theorem to represent the boundary traction field in terms of the boundary and field displacements in an integral form. Initially, we assume the unknown boundary conditions and deformations required to solve the problem. In this way we equate the work done by the exact solution (unknown) to the work done by an assumed solution. Discretizing the resulting equations and using an iterative procedure each step in the solution process becomes the solution to a well-posed problem. Thus, with sufficient perturbations the correct boundary conditions are reconstructed.

14083444
SoftCuts: A Soft Edge Smoothness Prior for Color Image Super-Resolution
Designing effective image priors is of great interest to image super-resolution (SR), which is a severely under-determined problem. An edge smoothness prior is favored since it is able to suppress the jagged edge artifact effectively. However, for soft image edges with gradual intensity transitions, it is generally difficult to obtain analytical forms for evaluating their smoothness. This paper characterizes soft edge smoothness based on a novel SoftCuts metric by generalizing the Geocuts method . The proposed soft edge smoothness measure can approximate the average length of all level lines in an intensity image. Thus, the total length of all level lines can be minimized effectively by integrating this new form of prior. In addition, this paper presents a novel combination of this soft edge smoothness prior and the alpha matting technique for color image SR, by adaptively normalizing image edges according to their alpha-channel description. This leads to the adaptive SoftCuts algorithm, which represents a unified treatment of edges with different contrasts and scales. Experimental results are presented which demonstrate the effectiveness of the proposed method.
8310892
Numerical meshfree path integration method for non-linear dynamic systems
Abstract We present a new numerical meshfree path integration (MPI) method for non-linear dynamic systems. The obtained MPI method can be performed in the irregular computational domain and the probability density values of the random nodes in the domain can be calculated via the MPI method and the ordinary differential equations for the first and second-order moments on the basis of Gaussian closure method. The piecewise linear interpolation based on adaptive least squares is utilized as a post processor to approximate the probability density values on arbitrary positions. The good performance of the resulting method is finally shown in the numerical examples by using three specific non-linear dynamic systems: Duffing oscillator subjected to both harmonic and stochastic excitations, Duffing–Rayleigh oscillator subjected to both harmonic and stochastic excitations, and CHEN system driven by three different Gaussian white noises.