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This paper illustrates the application of Wynn's vector ℇ-algorithm to solve a system of equations arising in the method of moments (MoM) solution of an electrostatic problem. Since the method is iterative, it does not require inversion of a matrix. The degree of accuracy of the solution can be controlled by specifying a convergence factor. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 378–380, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11223 [ABSTRACT FROM AUTHOR]

In this paper, we have proved in theory that the sign of the current stiffness matrix provides a correct indicator for determining the sign of the loading parameter in the arc-length algorithm before the first bifurcation point is encountered, but may not be the case thereafter. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses matrix approximation problems for matrices that are large, sparse, and/or representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques, possibly combined with random sampling. A multilevel coarsening technique is proposed, which utilizes a hypergraph associated with the data matrix and a graph coarsening strategy based on column matching. We consider a number of standard applications of this technique as well as a few new ones. Among standard applications, we first consider the problem of computing partial singular value decomposition, for which a combination of sampling and coarsening yields significantly improved singular value decomposition results relative to sampling alone. We also consider the column subset selection problem, a popular low‐rank approximation method used in data‐related applications, and show how multilevel coarsening can be adapted for this problem. Similarly, we consider the problem of graph sparsification and show how coarsening techniques can be employed to solve it. We also establish theoretical results that characterize the approximation error obtained and the quality of the dimension reduction achieved by a coarsening step, when a proper column matching strategy is employed. Numerical experiments illustrate the performances of the methods in a few applications. [ABSTRACT FROM AUTHOR]

In a very interesting recent paper, the authors proposed a least support denoising-orthogonal matching pursuit (LSD-OMP) algorithm and gave a sufficient condition for LSD-OMP algorithm in terms of restricted isometry constant of the measurement matrix. According to Dai and Milenkovic (2009), Wang et al. (2012) and Needell and Tropp (2009), this comment will point out that there are some errors in Tawfic and Kayhan (2015). [ABSTRACT FROM AUTHOR]

This is a new international journal "Numerical Linear Algebra With Applications," which publishes refereed papers describing significant developments in numerical linear algebra and the application of such method; to the solution of practical problems, such as occur in engineering, for instance. Numerical linear algebra algorithms form the core of almost any solution algorithm found in mathematical modeling. The models originate in physics, chemistry, engineering, ecology, economy and social sciences. Frequently they involve solutions of systems of algebraic equations and eigenvalue problems derived by some discretization method used for partial differential equations.