Search

In this paper, a lopsided modified Euler-extrapolated Hermitian and skew-Hermitian splitting (LME-HS) iteration method is introduced for solving the complex symmetric linear systems. Under a loose restriction on parameter θ, we demonstrate that LME-HS iteration method is convergent. Moreover, we present the optimal parameter θ* of the LME-HS method and discuss the spectral properties of corresponding preconditioned matrix. Finally, the numerical experiments are used to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

As is well known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing, signal processing, and so forth. In this paper, an algorithm on nonnegative matrix approximation is proposed. This method is mainly based on a relaxed active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. The method improves some recent results. In addition, some numerical experiments are presented in the synthetic data, imaging processing, and text clustering. By comparing with the other six nonnegative matrix approximation methods, this method is more robust in almost all cases. [ABSTRACT FROM AUTHOR]

As is well known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing, signal processing, and so forth. In this paper, an algorithm on nonnegative matrix approximation is proposed. This method is mainly based on a relaxed active set and the quasi-Newton type algorithm, by using the symmetric rankone and negative curvature direction technologies to approximate the Hessian matrix. The method improves some recent results. In addition, some numerical experiments are presented in the synthetic data, imaging processing, and text clustering. By comparing with the other six nonnegative matrix approximation methods, this method is more robust in almost all cases. [ABSTRACT FROM AUTHOR]

Some new upper and lower bounds on determinants are presented for diagonally dominant matrices and general H-matrices by using different methods. These bounds are some improvements of results given by Ostrowski (1952) and (1937), Price (1951), Wang and Zhang (2002), Huang and Liu (2005), and so forth. In addition, these bounds are also used to localize some numerical characters (e.g., the minimum eigenvalues, singular values and condition numbers) of certain matrices. [ABSTRACT FROM AUTHOR]

A matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row averages is called a B-matrix by J. M. Peña in References (SIAM J. Matrix Anal. Appl. 2001; 22:1027–1037) and (Numer. Math. 2003; 95:337–345). In this paper, it is generalized to more extended matrices—MB-matrices, which is proved to be a subclass of the class of P-matrices. Subsequently, we establish relationships between defined and some already known subclasses of P-matrices (see, References SIAM J. Matrix Anal. Appl. 2000; 21:67–78; Linear Algebra Appl. 2004; 393:353–364; Linear Algebra Appl. 1995; 225:117–123). As an application, some subclasses of P-matrices are used to localize the real eigenvalues of a real matrix. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, some optimal inclusion intervals of matrix singular values are discussed in the set ΩA of matrices equimodular with matrix A. These intervals can be obtained by extensions of the Gerschgorin-type theorem for singular values, based only on the use of positive scale vectors and their intersections. Theoretic analysis and numerical examples show that upper bounds of these intervals are optimal in some cases and lower bounds may be non-trivial (i.e. positive) when PA is a H-matrix, where P is a permutation matrix, which improves the conjecture in Reference (Linear Algebra Appl 1984; 56:105-119). Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The conjugate orthogonal conjugate gradient (COCG) method has been considered an attractive part of the Lanczos-type Krylov subspace method for solving complex symmetric linear systems. However, it is often faced with apparently irregular convergence behaviors in practical electromagnetic simulations. To avoid such a problem, the symmetric quasi-minimal residual (QMR) method has been developed. On the other hand, the conjugate A-orthogonal conjugate residual (COCR) method, which can be regarded as an extension of the conjugate residual method, also had been established. It shows that the COCR often gives smoother convergence behavior than the COCG method. The purpose of this paper is to apply the QMR approaches to the COCG and COCR to derive two new methods (including their preconditioned versions), and to report the benefits of the modified methods by some practical examples arising in electromagnetic simulations. [ABSTRACT FROM AUTHOR]